# Network Publications

Higgs boson decay into b-quarks at NNLO accuracy

Author / creator: Del Duca, Vittorio

Thu, 29 Jan 2015 04:19:27 GMT

CERN-PH-TH-2015-005

CP3-14-82

arXiv:1501.07226

JHEP 1504 (2015) 036

by: Del Duca, Vittorio (Frascati) et al.**Abstract:**

We compute the fully differential decay rate of the Standard Model Higgs boson into b-quarks at next-to-next-to-leading order (NNLO) accuracy in α$_{s}$. We employ a general subtraction scheme developed for the calculation of higher order perturbative corrections to QCD jet cross sections, which is based on the universal infrared factorization properties of QCD squared matrix elements. We show that the subtractions render the various contributions to the NNLO correction finite. In particular, we demonstrate analytically that the sum of integrated subtraction terms correctly reproduces the infrared poles of the two-loop double virtual contribution to this process. We present illustrative differential distributions obtained by implementing the method in a parton level Monte Carlo program. The basic ingredients of our subtraction scheme, used here for the first time to compute a physical observable, are universal and can be employed for the computation of more involved processes.
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Detailed record: *http://inspirehep.net/record/1341625*

Duality and modularity in elliptic integrable systems and vacua of $ \mathcal{N}={1}^{\ast } $ gauge theories

Author / creator: Bourget, Antoine

Thu, 22 Jan 2015 03:34:48 GMT

arXiv:1501.05074

JHEP 1504 (2015) 128

by: Bourget, Antoine (Ecole Normale Superieure) et al.**Abstract:**

We study complexified elliptic Calogero-Moser integrable systems. We determine the value of the potential at isolated extrema, as a function of the modular parameter of the torus on which the integrable system lives. We calculate the extrema for low rank B,C,D root systems using a mix of analytical and numerical tools. For so(5) we find convincing evidence that the extrema constitute a vector valued modular form for the Γ$_{0}$(4) congruence subgroup of the modular group. For so(7) and so(8), the extrema split into two sets. One set contains extrema that make up vector valued modular forms for congruence subgroups (namely Γ$_{0}$(4), Γ(2) and Γ(3)), and a second set contains extrema that exhibit monodromies around points in the interior of the fundamental domain. The former set can be described analytically, while for the latter, we provide an analytic value for the point of monodromy for so(8), as well as extensive numerical predictions for the Fourier coefficients of the extrema. Our results on the extrema provide a rationale for integrality properties observed in integrable models, and embed these into the theory of vector valued modular forms. Moreover, using the data we gather on the modularity of complexified integrable system extrema, we analyse the massive vacua of mass deformed $ \mathcal{N}=4 $ supersymmetric Yang-Mills theories with low rank gauge group of type B, C and D. We map out their transformation properties under the infrared electric-magnetic duality group as well as under triality for $ \mathcal{N}={1}^{\ast } $ with gauge algebra so(8). We compare the exact massive vacua on $ {\mathbb{R}}^3\times {S}^1 $ to those found in a semi-classical analysis on $ {\mathbb{R}}^4 $ . We identify several intriguing features of the quantum gauge theories.
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Detailed record: *http://inspirehep.net/record/1340484*

A Riemann-Hilbert formulation for the finite temperature Hubbard model

Author / creator: Cavaglià, Andrea

Wed, 21 Jan 2015 03:39:05 GMT

arXiv:1501.04651

JHEP 1506 (2015) 015

by: Cavaglià, Andrea (Turin U.) et al.**Abstract:**

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by J\"uttner, Kl\"umper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.
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Detailed record: *http://inspirehep.net/record/1340339*

Wilson Loops and Minimal Surfaces Beyond the Wavy Approximation

Author / creator: Dekel, Amit

Tue, 20 Jan 2015 04:07:30 GMT

NORDITA-2015-008

arXiv:1501.04202

JHEP 1503 (2015) 085

by: Dekel, Amit (Nordita)**Abstract:**

We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space. We use a formalism introduced recently by Kruczenski to perturbatively compute the area corresponding to boundary contours which are deformations of the circle. Our perturbative expansion is carried to high orders compared with the wavy approximation and yields new analytic results. The regularized area is invariant under a one parameter family of continuous deformations of the boundary contour which are not related to the global symmetry of the problem. We show that this symmetry of the Wilson loops breaks at weak coupling at an a priori unexpected order in the perturbative expansion. We also study the corresponding Lax operator and algebraic curve for these solutions.
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Detailed record: *http://inspirehep.net/record/1340119*

Vacuum stability of asymptotically safe gauge-Yukawa theories

Author / creator: Litim, Daniel F.

Wed, 14 Jan 2015 05:40:34 GMT

CP3-ORIGINS-2014-049

DIAS-2014-049

NORDITA-2014-145

arXiv:1501.03061

JHEP 1601 (2016) 081

by: Litim, Daniel F. (Sussex U.) et al.**Abstract:**

We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established.
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Detailed record: *http://inspirehep.net/record/1338592*

3d mirror symmetry as a canonical transformation

Author / creator: Drukker, Nadav

Tue, 13 Jan 2015 03:39:36 GMT

arXiv:1501.02268

JHEP 1505 (2015) 004

by: Drukker, Nadav (King's Coll. London, Dept. Math) et al.**Abstract:**

We generalize the free Fermi-gas formulation of certain 3d $ \mathcal{N}=3 $ super-symmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition functions are given by simple modifications of the argument of the Airy function found previously. With these extra parameters it is easy to see that mirror-symmetry corresponds to linear canonical transformations on the phase space (or operator algebra) of the 1-dimensional fermions.
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Detailed record: *http://inspirehep.net/record/1338376*

Exact Results in Supersymmetric Gauge Theories

Author / creator: Valatka, Saulius

Mon, 05 Jan 2015 03:46:17 GMT

arXiv:1501.00111

by: Valatka, Saulius (King's Coll. London, Dept. Math)**Abstract:**

In this thesis we discuss supersymmetric gauge theories, focusing on exact results achieved using methods of integrability. For the larger portion of the thesis we study the N=4 super Yang-Mills theory in the planar limit, a recurring topic being the Konishi anomalous dimension, which is roughly the analogue for the mass of the proton in quantum chromodynamics. The N=4 supersymmetric Yang-Mills theory is known to be integrable in the planar limit, which opens up a wealth of techniques one can employ in order to find results in this limit valid at any value of the coupling. We begin with perturbation theory where the integrability of the theory first manifests itself. Here we showcase the first exact result, the so-called slope function, which is the linear small spin expansion coefficient of the generalized Konishi anomalous dimension. We then move on to exact results mainly achieved using the novel quantum spectral curve approach, the method allowing one to find scaling dimensions of operators at arbitrary values of the coupling. As an example we find the second coefficient in the small spin expansion after the slope, which we call the curvature function. This allows us to extract non-trivial information about the Konishi operator. Methods of integrability are also applicable to other supersymmetric gauge theories such as ABJM, which in fact shares many similarities with N=4 super Yang-Mills. We briefly review these parallel developments in the last chapter of the thesis.
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Detailed record: *http://inspirehep.net/record/1336107*

Correlation functions of the chiral stress-tensor multiplet in $ \mathcal{N}=4 $ SYM

Author / creator: Chicherin, Dmitry

Wed, 31 Dec 2014 03:40:54 GMT

CERN-PH-TH-2014-270

DCPT-14-79

HU-EP-14-66

IPHT-T14-242

LAPTH-239-14

arXiv:1412.8718

JHEP 1506 (2015) 198

by: Chicherin, Dmitry (Annecy, LAPTH) et al.**Abstract:**

We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.
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Detailed record: *http://inspirehep.net/record/1335848*

Graßmannian integrals as matrix models for non-compact Yangian invariants

Author / creator: Kanning, Nils

Wed, 31 Dec 2014 03:40:11 GMT

HU-MATHEMATIK-2014-38

HU-EP-14-63

AEI-2014-065

arXiv:1412.8476

Nucl.Phys. B894 (2015) 407-421

by: Kanning, Nils (Humboldt U., Berlin, Inst. Math.) et al.**Abstract:**

In the past years, there have been tremendous advances in the field of planar N=4 super Yang–Mills scattering amplitudes. At tree-level they were formulated as Graßmannian integrals and were shown to be invariant under the Yangian of the superconformal algebra psu(2,2|4) . Recently, Yangian invariant deformations of these integrals were introduced as a step towards regulated loop-amplitudes. However, in most cases it is still unclear how to evaluate these deformed integrals. In this work, we propose that changing variables to oscillator representations of psu(2,2|4) turns the deformed Graßmannian integrals into certain matrix models. We exemplify our proposal by formulating Yangian invariants with oscillator representations of the non-compact algebra u(p,q) as Graßmannian integrals. These generalize the Brezin–Gross–Witten and Leutwyler–Smilga matrix models. This approach might make elaborate matrix model technology available for the evaluation of Graßmannian integrals. Our invariants also include a matrix model formulation of the u(p,q) R-matrix, which generates non-compact integrable spin chains.
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Detailed record: *http://inspirehep.net/record/1335830*

Form factor relocalisation and interpolating renormalisation group flows from the staircase model

Author / creator: Dorey, Patrick

Tue, 30 Dec 2014 04:12:11 GMT

DCPT-14-81

arXiv:1412.8442

DCPT--14-81

JHEP 1503 (2015) 054

by: Dorey, Patrick (Durham U., Dept. of Math.) et al.**Abstract:**

We investigate the staircase model, introduced by Aliosha Zamolodchikov through an analytic continuation of the sinh-Gordon S-matrix to describe interpolating flows between minimal models of conformal field theory in two dimensions. Applying the form factor expansion and the c-theorem, we show that the resulting c-function has the same physical content as that found by Zamolodchikov from the thermodynamic Bethe Ansatz. This turns out to be a consequence of a nontrivial underlying mechanism, which leads to an interesting localisation pattern for the spectral integrals giving the multi-particle contributions. We demonstrate several aspects of this form factor relocalisation, which suggests a novel approach to the construction of form factors and spectral sums in integrable renormalisation group flows with non-diagonal scattering.
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Detailed record: *http://inspirehep.net/record/1335757*

Exact finite volume expectation values of local operators in excited states

Author / creator: Pozsgay, B.

Tue, 30 Dec 2014 04:12:11 GMT

arXiv:1412.8436

JHEP 1504 (2015) 023

by: Pozsgay, B. (Hungarian Acad. Sci., Budapest) et al.**Abstract:**

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.
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Detailed record: *http://inspirehep.net/record/1335756*

Entanglement negativity and entropy in non-equilibrium conformal field theory

Author / creator: Hoogeveen, Marianne

Thu, 25 Dec 2014 03:40:25 GMT

arXiv:1412.7568

Nucl.Phys. B898 (2015) 78-112

by: Hoogeveen, Marianne (King's Coll. London, Dept. Math) et al.**Abstract:**

We study the dynamics of the entanglement in one-dimensional critical quantum systems after a local quench in which two independently thermalized semi-infinite halves are joined to form a homogeneous infinite system and left to evolve unitarily. We show that under certain conditions a nonequilibrium steady state (NESS) is reached instantaneously as soon as the entanglement interval is within the light cone emanating from the contact point. In this steady state, the exact expressions for the entanglement entropy and the logarithmic negativity are in agreement with the steady state density matrix being a boosted thermal state, as expected. We derive various general identities: relating the negativity after the quench with unequal left and right initial temperatures with that where the left and right temperatures are equal; and relating these with the negativity in equilibrium thermal states. In certain regimes the resulting expressions can be analytically evaluated. Immediately after the interval intersects the light cone, we find logarithmic growth. For a very long interval, we find that the negativity approaches a plateau after sufficiently long times, different from its NESS value. The NESS value is reached instantly as soon as the entire interval is contained in the light cone. This provides a theoretical framework explaining recently obtained numerical results.
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Detailed record: *http://inspirehep.net/record/1335517*

The $ \mathcal{N}=2 $ superconformal bootstrap

Author / creator: Beem, Christopher

Thu, 25 Dec 2014 03:40:20 GMT

arXiv:1412.7541

HU-EP-14-61

YITP-SB-14-54

CERN-PH-TH-2014-269

HU-EP-14/61

JHEP 1603 (2016) 183

by: Beem, Christopher (Princeton, Inst. Advanced Study) et al.**Abstract:**

In this work we initiate the conformal bootstrap program for $ \mathcal{N}=2 $ super-conformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of $ \mathcal{N}=2 $ chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any $ \mathcal{N}=2 $ superconformal field theory.
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Detailed record: *http://inspirehep.net/record/1335515*

Comments on the Casimir energy in supersymmetric field theories

Author / creator: Lorenzen, Jakob

Wed, 24 Dec 2014 03:49:32 GMT

arXiv:1412.7463

JHEP 1507 (2015) 001

by: Lorenzen, Jakob (King's Coll. London, Dept. Math) et al.**Abstract:**

We study the Casimir energy of four-dimensional supersymmetric gauge theories in the context of the rigid limit of new minimal supergravity. Firstly, revisiting the computation of the localized partition function on S$^{1}$ × S$^{3}$, we recover the supersymmetric Casimir energy from its path integral definition. Secondly, we consider the same theories in the Hamiltonian formalism on $ \mathbb{R}\times {S}^3 $ , focussing on the free limit and including a one- parameter family of background gauge fields along $ \mathbb{R} $ . We compute the vacuum expectation value of the canonical Hamiltonian using zeta function regularization, and show that this interpolates between the supersymmetric Casimir energy and the ordinary Casimir energy of a supersymmetric free field theory.
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Detailed record: *http://inspirehep.net/record/1335453*

Exact Results on $\mathcal{N} =$ 2 Supersymmetric Gauge Theories

Author / creator: Teschner, Jörg

Tue, 23 Dec 2014 04:04:03 GMT

arXiv:1412.7145

by: Teschner, Jörg (DESY)**Abstract:**

This is the introduction to the collection of review articles "Exact results on N=2 supersymmetric gauge theories". The first three sections are intended to give a general overview over the physical motivations behind this direction of research, and some of the developments that initiated this project. These sections are written for a broad audience of readers with interest in quantum field theory, assuming only very basic knowledge of supersymmetric gauge theories and string theory. This will be followed by a brief overview over the different chapters collected in this volume, while the last section indicates some related developments that we were unfortunately not able to cover.
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Detailed record: *http://inspirehep.net/record/1335348*

Supersymmetric gauge theories, quantisation of moduli spaces of flat connections, and Liouville theory

Author / creator: Teschner, Jörg

Tue, 23 Dec 2014 04:04:00 GMT

arXiv:1412.7140

by: Teschner, Jörg (DESY)**Abstract:**

This is the 11th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. It describes an approach to understanding the 4d/2d relations discovered by Alday, Gaiotto and Tachikawa by establishing a triangle of relations between the zero mode quantum mechanics obtained by localisation of class $\cal S$ theories, the quantum theory obtained by quantisation of Hitchin moduli spaces, and conformal field theory.
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Detailed record: *http://inspirehep.net/record/1335347*

Generalised double-logarithmic equation in QCD

Author / creator: Velizhanin, V.N.

Tue, 23 Dec 2014 04:02:23 GMT

HU-EP-14-62

HU-MATHEMATIK-2014-40

arXiv:1412.7143

Mod.Phys.Lett. A32 (2017) 1750213

by: Velizhanin, V.N. (Humboldt U., Berlin)**Abstract:**

We present a generalisation of the double-logarithmic equation for the anomalous dimension of the non-singlet unpolarized twist-2 operators in QCD. Using the known three-loop result, this generalisation allows to predict a small x expansion of the four-loop non-singlet splitting functions in QCD for all powers of logarithms up to the single-logarithm term.
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Detailed record: *http://inspirehep.net/record/1335311*

D-brane solitons in various dimensions

Author / creator: Gudnason, Sven Bjarke

Tue, 23 Dec 2014 04:02:13 GMT

NORDITA-2014-144

arXiv:1412.6995

Phys.Rev. D91 (2015) 045018

by: Gudnason, Sven Bjarke (Nordita) et al.**Abstract:**

We construct a D-brane soliton, a composite topological soliton sharing some properties with a D-brane, in a Skyrme model in 4+1 dimensions, in which Skyrmions are strings ending on a domain wall. We further generalize this D-brane soliton to diverse dimensions. A string, carrying the $\pi_{N-1}$ topological charge, ends on a domain wall in an O(N) model with higher-derivative terms in N+1 dimensions.
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Detailed record: *http://inspirehep.net/record/1335302*

Off-shell scalar products for the $XXZ$ spin chain with open boundaries

Author / creator: Galleas, W.

Thu, 18 Dec 2014 03:51:12 GMT

arXiv:1412.5389

Nucl.Phys. B893 (2015) 346-375

by: Galleas, W. (Hamburg U., Inst. Theor. Phys. II)**Abstract:**

In this work we study scalar products of Bethe vectors associated with the XXZ spin chain with open boundary conditions. The scalar products are obtained as solutions of a system of functional equations. The description of scalar products through functional relations follows from a particular map having the reflection algebra as its domain and a function space as the codomain. Within this approach we find a multiple contour integral representation for the scalar products in which the homogeneous limit can be obtained trivially.
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Detailed record: *http://inspirehep.net/record/1334727*

Double Wick rotating Green-Schwarz strings

Author / creator: Arutyunov, Gleb

Wed, 17 Dec 2014 03:52:21 GMT

arXiv:1412.5137

JHEP 1505 (2015) 027

by: Arutyunov, Gleb (Hamburg U.) et al.**Abstract:**

Via an appropriate field redefinition of the fermions, we find a set of conditions under which light cone gauge fixed world sheet theories of strings on two different backgrounds are related by a double Wick rotation. These conditions take the form of a set of transformation laws for the background fields, complementing a set of transformation laws for the metric and B field we found previously with a set for the dilaton and RR fields, and are compatible with the supergravity equations of motion. Our results prove that at least to second order in fermions, the AdS$_{5}$ × S$^{5}$ mirror model which plays an important role in the field of integrability in AdS/CFT, represents a string on ‘mirror AdS$_{5}$ × S$^{5}$’, the background that follows from our transformations. We discuss analogous solutions for AdS$_{3}$ × S$^{3}$ × T$^{4}$ and AdS$_{2}$ × S$^{2}$ × T$^{6}$. The main ingredient in our derivation is the light cone gauge fixed action for a string on an (almost) completely generic background, which we explicitly derive to second order in fermions.
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Detailed record: *http://inspirehep.net/record/1334563*

Extrapolating W-Associated Jet-Production Ratios at the LHC

Author / creator: Bern, Z.

Wed, 17 Dec 2014 03:50:55 GMT

SLAC-PUB-16144

UCLA-14-TEP-108

IPPP-11-82

SB-F-442-14

SACLAY-IPHT-T14-185

FR-PHENO-2014-002

arXiv:1412.4775

SLAC--PUB--16144

SACLAY--IPHT--T14-185

Phys.Rev. D92 (2015) 014008

by: Bern, Z. (UCLA) et al.**Abstract:**

Electroweak vector-boson production, accompanied by multiple jets, is an important background to searches for physics beyond the standard model. A precise and quantitative understanding of this process is helpful in constraining deviations from known physics. We study four key ratios in W+n-jet production at the LHC. We compute the ratio of cross sections for W+n- to W+(n-1)-jet production as a function of the minimum jet transverse momentum. We also study the ratio differentially, as a function of the W-boson transverse momentum; as a function of the scalar sum of the jet transverse energy, HTjets; and as a function of certain jet transverse momenta. We show how to use such ratios to extrapolate differential cross sections to W+6-jet production at next-to-leading order, and we cross-check the method against a direct calculation at leading order. We predict the differential distribution in HTjets for W+6 jets at next-to-leading order using such an extrapolation. We use the BlackHat software library together with SHERPA to perform the computations.
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Detailed record: *http://inspirehep.net/record/1334533*

Six-loop anomalous dimension of twist-two operators in planar $ \mathcal{N}=4 $ SYM theory

Author / creator: Marboe, Christian

Tue, 16 Dec 2014 04:39:16 GMT

HU-MATHEMATIK-P-2014-37

HU-EP-14-60

arXiv:1412.4762

JHEP 1507 (2015) 084

by: Marboe, Christian (Trinity Coll., Dublin) et al.**Abstract:**

We compute the general form of the six-loop anomalous dimension of twist-two operators with arbitrary spin in planar N=4 SYM theory. First we find the contribution from the asymptotic Bethe ansatz. Then we reconstruct the wrapping terms from the first 35 even spin values of the full six-loop anomalous dimension computed using the quantum spectral curve approach. The obtained anomalous dimension satisfies all known constraints coming from the BFKL equation, the generalised double-logarithmic equation, and the small spin expansion.
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Detailed record: *http://inspirehep.net/record/1334390*

Toda 3-Point Functions From Topological Strings II

Author / creator: Isachenkov, Mikhail

Thu, 11 Dec 2014 03:42:53 GMT

DESY-14-236

HU-MATHEMATIK-35-2014

HU-EP-14-57

arXiv:1412.3395

JHEP 1608 (2016) 066

by: Isachenkov, Mikhail (DESY) et al.**Abstract:**

In [1] we proposed a formula for the 3-point structure constants of generic primary fields in the Toda field theory, derived using topological strings and the AGT-W correspondence from the partition functions of the non-Lagrangian T$_{N}$ theories on S$^{4}$. In this article, we obtain from it the well-known formula by Fateev and Litvinov and show that the degeneration on a first level of one of the three primary fields on the Toda side corresponds to a particular Higgsing of the T$_{N}$ theories.
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Detailed record: *http://inspirehep.net/record/1333700*

Q-operators, Yangian invariance and the quantum inverse scattering method

Author / creator: Frassek, Rouven

Thu, 11 Dec 2014 03:42:40 GMT

arXiv:1412.3339

by: Frassek, Rouven (Durham U., Dept. of Math.)**Abstract:**

Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author's original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the functional relations among them. We study how the nearest-neighbor Hamiltonian and in principle also higher local charges can be extracted from the Q-operators directly. Secondly, we formulate the Yangian invariance condition, also studied in relation to scattering amplitudes of N=4 super Yang-Mills theory, in the RTT-realization. We find that Yangian invariants can be interpreted as special eigenvectors of certain inhomogeneous spin chains. This allows us to apply the algebraic Bethe ansatz and derive the corresponding Bethe equations that are relevant to construct the invariants. We examine the connection between the Yangian invariant spin chain eigenstates whose components can be understood as partition functions of certain 2d lattice models and tree-level scattering amplitudes of the four-dimensional gauge theory. Finally, we conclude and discuss some future directions.
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Detailed record: *http://inspirehep.net/record/1333697*

Integral pentagon relations for 3d superconformal indices

Author / creator: Gahramanov, Ilmar

Wed, 10 Dec 2014 03:37:44 GMT

HU-EP-14-59

arXiv:1412.2926

Proc.Symp.Pure Math. 93 (2016) 165-173

by: Gahramanov, Ilmar (Humboldt U., Berlin) et al.**Abstract:**

The superconformal index of a three-dimensional supersymmetric field theory can be expressed in terms of basic hypergeometric integrals. By comparing the indices of dual theories, one can find new integral identities for basic hypergeometric integrals. Some of these integral identities have the form of the pentagon identity which can be interpreted as the 2-3 Pachner move for triangulated 3-manifolds.
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Detailed record: *http://inspirehep.net/record/1333424*

last update 2014/11/27