# Fellow Publications

Spectra of Sigma Models on Semi-Symmetric Spaces

Author / creator: Cagnazzo, Alessandra

Thu, 24 Dec 2015 03:39:04 GMT

DESY-14-229

NORDITA-2015-140

arXiv:1512.07472

Nucl.Phys. B906 (2016) 342-366

by: Cagnazzo, Alessandra (DESY) et al.**Abstract:**

Sigma models on semi-symmetric spaces provide the central building block for string theories on AdS backgrounds. Under certain conditions on the global supersymmetry group they can be made one-loop conformal by adding an appropriate fermionic Wess–Zumino term. We determine the full one-loop dilation operator of the theory. It involves an interesting new XXZ-like interaction term. Eigenvalues of our dilation operator, i.e. the one-loop anomalous dimensions, are computed for a few examples.
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Detailed record: *http://inspirehep.net/record/1411260*

Exact Zero Vacuum Energy in twisted SU(N) Principal Chiral Field

Author / creator: Leurent, Sebastien

Mon, 30 Nov 2015 04:01:17 GMT

arXiv:1511.08491

DESY-15-233

by: Leurent, Sebastien (Bourgogne U.) et al.**Abstract:**

We present a finite set of equations for twisted PCF model. At the special twist in the root of unity we demonstrate that the vacuum energy is exactly zero at any size L. Also in SU(2) case we numerically calculate the energy of the single particle state with zero rapidity, as a function of L.
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Detailed record: *http://inspirehep.net/record/1406983*

Diagonal form factors and hexagon form factors

Author / creator: Jiang, Yunfeng

Fri, 20 Nov 2015 03:42:52 GMT

arXiv:1511.06199

JHEP 1607 (2016) 120

by: Jiang, Yunfeng (Zurich, ETH) et al.**Abstract:**

We study the heavy-heavy-light (HHL) three-point functions in the planar $ \mathcal{N} $ = 4 super-Yang-Mills theory using the recently proposed hexagon bootstrap program [1]. We prove the conjecture of Bajnok, Janik and Wereszczynski [2] on the polynomial L-dependence of HHL structure constant up to the leading finite-size corrections, where L is the length of the heavy operators. The proof is presented for a specific set-up but the method can be applied to more general situations.
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Detailed record: *http://inspirehep.net/record/1405472*

Three-point correlator of twist-2 light-ray operators in N=4 SYM in BFKL approximation

Author / creator: Balitsky, Ian

Thu, 12 Nov 2015 03:45:28 GMT

arXiv:1511.03625

DESY-15-211

JLAB-THY-15-2161

by: Balitsky, Ian (Old Dominion U.) et al.**Abstract:**

We present calculation of the correlation function of three twist-2 operators in the BFKL limit. The calculation is performed in N = 4 SYM but the result is valid in other gauge theories such as QCD. The obtained leading order structure constant is exact for any number of colors.
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Detailed record: *http://inspirehep.net/record/1404026*

The $\mathcal{N}=2$ Schur index from free fermions

Author / creator: Bourdier, Jun

Tue, 27 Oct 2015 03:54:02 GMT

arXiv:1510.07041

JHEP 1601 (2016) 167

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

We study the Schur index of 4-dimensional $ \mathcal{N}=2 $ circular quiver theories. We show that the index can be expressed as a weighted sum over partition functions describing systems of free Fermions living on a circle. For circular SU (N) quivers of arbitrary length we evaluate the large N limit of the index, up to exponentially suppressed corrections. For the single node theory ( $ \mathcal{N}=4 $ SYM) and the two node quiver we are able to go beyond the large N limit, and obtain the complete, all orders large N expansion of the index, as well as explicit finite N results in terms of elliptic functions.
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Detailed record: *http://inspirehep.net/record/1400846*

Quantum Spectral Curve for a cusped Wilson line in $ \mathcal{N}=4 $ SYM

Author / creator: Gromov, Nikolay

Fri, 09 Oct 2015 02:40:25 GMT

arXiv:1510.02098

JHEP 1604 (2016) 134

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

We show that the Quantum Spectral Curve (QSC) formalism, initially formulated for the spectrum of anomalous dimensions of all local single trace operators in $ \mathcal{N}=4 $ SYM, can be extended to the generalized cusp anomalous dimension for all values of the parameters. We find that the large spectral parameter asymptotics and some analyticity properties have to be modified, but the functional relations are unchanged. As a demonstration, we find an all-loop analytic expression for the first two nontrivial terms in the small |ϕ ± θ| expansion. We also present nonperturbative numerical results at generic angles which match perfectly 4-loop perturbation theory and the classical string prediction.
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Detailed record: *http://inspirehep.net/record/1396749*

Q-operators for the open Heisenberg spin chain

Author / creator: Frassek, Rouven

Thu, 17 Sep 2015 02:45:54 GMT

arXiv:1509.04867

Nucl.Phys. B901 (2015) 229-248

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

We construct Q-operators for the open spin- 12 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang–Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.
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Detailed record: *http://inspirehep.net/record/1393690*

OPE for all Helicity Amplitudes II. Form Factors and Data Analysis

Author / creator: Basso, Benjamin

Thu, 13 Aug 2015 02:40:13 GMT

arXiv:1508.02987

JHEP 1512 (2015) 088

by: Basso, Benjamin (Ecole Normale Superieure) et al.**Abstract:**

We present the general flux tube integrand for MHV and non-MHV amplitudes, in planar $ \mathcal{N}=4 $ SYM theory, up to a group theoretical rational factor. We find that the MHV and non-MHV cases only differ by simple form factors which we derive. This information allows us to run the operator product expansion program for all sorts of non-MHV amplitudes and to test the recently proposed map with the so called charged pentagons transitions. Perfect agreement is found, on a large sample of non-MHV amplitudes, with the perturbative data available in the literature.
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Detailed record: *http://inspirehep.net/record/1387663*

Soft Pomeron in Holographic QCD

Author / creator: Ballon-Bayona, Alfonso

Tue, 04 Aug 2015 03:04:29 GMT

CERN-PH-TH-2015-180

arXiv:1508.00008

Phys.Rev. D93 (2016) 035005

by: Ballon-Bayona, Alfonso (Porto U.) et al.**Abstract:**

We study the graviton Regge trajectory in holographic QCD as a model for high energy scattering processes dominated by soft-Pomeron exchange. This is done by considering spin J fields from the closed string sector that are dual to glueball states of even spin and parity. In particular, we construct a model that governs the analytic continuation of the spin J field equation to the region of real J<2, which includes the scattering domain of the negative Maldelstam variable t. The model leads to approximately linear Regge trajectories and is compatible with the measured values of 1.08 for the intercept and 0.25 GeV−2 for the slope of the soft Pomeron. The intercept of the secondary Pomeron trajectory is in the same region of the subleading trajectories, made of mesons, proposed by Donnachie and Landshoff, and should therefore be taken into account.
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Detailed record: *http://inspirehep.net/record/1386264*

The exact Schur index of $\mathcal{N}=4$ SYM

Author / creator: Bourdier, Jun

Mon, 03 Aug 2015 03:05:06 GMT

arXiv:1507.08659

JHEP 1511 (2015) 210

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

The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least $ \mathcal{N}=2 $ supersymmetry in four dimensions is a particular refinement of the index, dependent on one parameter q serving as the fugacity for a particular set of charges which commute with the hamiltonian and some supersymmetry generators. This index has a known expression for all Lagrangian and some non-Lagrangian theories as a finite dimensional integral or a complicated infinite sum. In the case of $ \mathcal{N}=2 $ SYM with gauge group U(N ) we rewrite this as the partition function of a gas of N non interacting and translationally invariant fermions on a circle. This allows us to perform the integrals and write down explicit expressions for fixed N as well as the exact all orders large N expansion.
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Detailed record: *http://inspirehep.net/record/1385900*

Pomeron Eigenvalue at Three Loops in $\mathcal N=$ 4 Supersymmetric Yang-Mills Theory

Author / creator: Gromov, Nikolay

Thu, 16 Jul 2015 03:08:26 GMT

arXiv:1507.04010

Phys.Rev.Lett. 115 (2015) 251601

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

We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4 using Quantum Spectral Curve (QSC) integrability based method. The result is verified with more than 60 digits precision using the numerical method developed by us in a previous paper. As a byproduct we developed a general analytic method of solving the QSC perturbatively.
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Detailed record: *http://inspirehep.net/record/1382961*

On-shell diagrams, Graßmannians and integrability for form factors

Author / creator: Frassek, Rouven

Mon, 29 Jun 2015 02:59:42 GMT

HU-MATH-2015-10

HU-EP-15-30

DCPT-15-37

arXiv:1506.08192

JHEP 1601 (2016) 182

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

We apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4 SYM theory to tree-level form factors of this theory. Focussing on the colour-ordered super form factors of the chiral part of the stress-tensor multiplet as an example, we show how to systematically construct on-shell diagrams for these form factors with the minimal form factor as further building block in addition to the three-point amplitudes. Moreover, we obtain analytic representations in terms of Gra{\ss}mannian integrals in spinor helicity, twistor and momentum twistor variables. While Yangian invariance is broken by the operator insertion, we find that the form factors are eigenstates of the integrable spin-chain transfer matrix built from the monodromy matrix that yields the Yangian generators. Constructing them via the method of R operators allows to introduce deformations that preserve the integrable structure. We finally show that the integrable properties extend to minimal tree-level form factors of generic composite operators as well as certain leading singularities of their n-point loop-level form factors.
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Detailed record: *http://inspirehep.net/record/1379993*

Structure constant of twist-2 light-ray operators in the Regge limit

Author / creator: Balitsky, Ian

Tue, 09 Jun 2015 03:42:20 GMT

LPTENS-15-01

DESY-15-086

JLAB-THY-15-2053

arXiv:1506.02038

Phys.Rev. D93 (2016) 061701

by: Balitsky, Ian (Old Dominion U.) et al.**Abstract:**

We compute the normalized structure constant of three twist-2 operators in N=4 SYM in the leading Balitsky-Fadin-Kuraev-Lipatov (BFKL) approximation at any Nc. The result is applicable to other gauge theories including QCD.
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Detailed record: *http://inspirehep.net/record/1375055*

Conceptual design of elliptical cavities for intensity and position sensitive beam measurements in storage rings

Author / creator: Sanjari, M.S.

Tue, 02 Jun 2015 02:56:16 GMT

arXiv:1506.00440

Phys.Scripta T166 (2015) 014060

by: Sanjari, M.S.**Abstract:**

Position sensitive beam monitors are indispensable for the beam diagnostics in storage rings. Apart from their applications in the measurements of beam parameters, they can be used in non-destructive in-ring decay studies of radioactive ion beams as well as enhancing precision in the isochronous mass measurement technique. In this work, we introduce a novel approach based on cavities with elliptical cross-section, in order to compensate the limitations of known designs for the application in ion storage rings. The design is aimed primarily for future heavy ion storage rings of the FAIR project. The conceptual design is discussed together with simulation results.
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Detailed record: *http://inspirehep.net/record/1373976*

The $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ worldsheet S matrix

Author / creator: Borsato, Riccardo

Tue, 02 Jun 2015 02:53:19 GMT

ITP-UU-15-08

HU-EP-15-26

HU-MATHEMATIK-P-2015-06

IMPERIAL-TP-OOS-2015-01

arXiv:1506.00218

J.Phys. A48 (2015) 415401

by: Borsato, Riccardo (Utrecht U.) et al.**Abstract:**

We investigate type IIB strings on $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ with mixed Ramond-Ramond (R-R) and Neveu-Schwarz-Neveu-Schwarz (NS-NS) flux. By suitably gauge-fixing the closed string Green-Schwarz (GS) action of this theory, we derive the off-shell symmetry algebra and its representations. We use these to determine the non-perturbative worldsheet S-matrix of fundamental excitations in the theory. The analysis involves both massive and massless modes in complete generality. The S-matrix we find involves a number of phase factors, which in turn satisfy crossing equations that we also determine. We comment on the nature of the heaviest modes of the theory, but leave their identification either as composites or bound-states to a future investigation.
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Detailed record: *http://inspirehep.net/record/1373956*

Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling

Author / creator: Hollo, Laszlo

Tue, 28 Apr 2015 05:51:40 GMT

arXiv:1504.07133

JHEP 1509 (2015) 125

by: Hollo, Laszlo (Wigner RCP, Budapest) et al.**Abstract:**

In this paper we consider a special kind of three-point functions of HHL type at weak coupling in $ \mathcal{N}=4 $ SYM theory and analyze its volume dependence. At strong coupling this kind of three-point functions were studied recently by Bajnok, Janik and Wereszczynski [1]. The authors considered some cases of HHL correlator in the $ \mathfrak{s}\mathfrak{u}(2) $ sector and, relying on their explicit results, formulated a conjecture about the form of the volume dependence of the symmetric HHL structure constant to be valid at any coupling up to wrapping corrections. In order to test this hypothesis we considered the HHL correlator in $ \mathfrak{s}\mathfrak{u}(2) $ sector at weak coupling and directly showed that, up to one loop, the finite volume dependence has exactly the form proposed in [1]. Another side of the conjecture suggests that computation of the symmetric structure constant is equivalent to computing the corresponding set of infinite volume form factors, which can be extracted as the coefficients of finite volume expansion. In this sense, extracting appropriate coefficients from our result gives a prediction for the corresponding infinite volume form factors.
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Detailed record: *http://inspirehep.net/record/1364924*

Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4

Author / creator: Gromov, Nikolay

Tue, 28 Apr 2015 05:51:22 GMT

arXiv:1504.06640

JHEP 1606 (2016) 036

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

We developed an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar $ \mathcal{N} $ = 4 Super-Yang-Mills at finite coupling. The method is based on the Quantum Spectral Curve formalism. In contrast to Thermodynamic Bethe Ansatz, worked out only for some very special operators, this method is applicable for generic states/operators and is much faster and more precise due to its Q-quadratic convergence rate.
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Detailed record: *http://inspirehep.net/record/1364918*

Algebraic Bethe ansatz for Q-operators: The Heisenberg spin chain

Author / creator: Frassek, Rouven

Mon, 20 Apr 2015 02:40:11 GMT

arXiv:1504.04501

J.Phys. A48 (2015) 294002

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

We diagonalize Q-operators for rational homogeneous ${\mathfrak{sl}}(2)$-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang–Baxter equation we demonstrate that the Q-operators act diagonally on the Bethe vectors if the Bethe equations are satisfied. In this way we provide a direct proof that the eigenvalues of the Q-operators studied here are given by Baxter's Q-functions.
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Detailed record: *http://inspirehep.net/record/1361922*

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*

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*

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*

From Spin Vertex to String Vertex

Author / creator: Jiang, Yunfeng

Tue, 09 Dec 2014 03:58:26 GMT

arXiv:1412.2256

JHEP 1506 (2015) 172

by: Jiang, Yunfeng (IPhT, Saclay) et al.**Abstract:**

In the recent publication arXiv:1410.8860 the spin vertex was introduced as a new approach for computing three-point functions in N = 4 SYM. In this note we consider the BMN limit of the spin vertex for scalar excitations and show that it reproduces the string vertex in the light-cone string field theory which describes the string interactions in the pp-wave background at the leading order of BMN expansion. This is achieved by introducing a polynomial representation for the spin vertex. We derive the Neumann coefficients from the spin vertex at weak coupling and show they match with the Neumann coefficients from the string field theory.
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Detailed record: *http://inspirehep.net/record/1333260*

OPE for all Helicity Amplitudes

Author / creator: Basso, Benjamin

Thu, 04 Dec 2014 03:51:31 GMT

arXiv:1412.1132

JHEP 1508 (2015) 018

by: Basso, Benjamin (Ecole Normale Superieure) et al.**Abstract:**

We extend the Operator Product Expansion (OPE) for scattering amplitudes in planar $ \mathcal{N}=4 $ SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity configurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pentagons entering MHV amplitudes and they can be bootstrapped at finite coupling from the integrable dynamics of the color flux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture.
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Detailed record: *http://inspirehep.net/record/1332533*

On Classical Solutions of 4d Supersymmetric Higher Spin Theory

Author / creator: Bourdier, Jun

Thu, 27 Nov 2014 03:45:21 GMT

arXiv:1411.7037

JHEP 1504 (2015) 097

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

We present a simple construction of solutions to the supersymmetric higher spin theory based on solutions to bosonic theories. We illustrate this for the case of the Didenko-Vasiliev solution in arXiv:0906.3898, for which we have found a striking simplification where the higher-spin connection takes the vacuum value. Studying these solutions further, we check under which conditions they preserve some supersymmetry in the bulk, and when they are compatible with the boundary conditions conjectured to be dual to certain 3d SUSY Chern-Simons-matter theories. We perform the analysis for a variety of theories with $ \mathcal{N} $ = 2, $ \mathcal{N} $ = 3, $ \mathcal{N} $ = 4 and $ \mathcal{N} $ = 6 and find a rich spectrum of 1/4, 1/3 and 1/2-BPS solutions.
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Detailed record: *http://inspirehep.net/record/1330327*

Integrability and the Conformal Field Theory of the Higgs branch

Author / creator: Ohlsson Sax, Olof

Fri, 14 Nov 2014 05:29:15 GMT

IMPERIAL-TP-OOS-2014-05

HU-MATHEMATIK-2014-33

HU-EP-14-49

arXiv:1411.3676

JHEP 1506 (2015) 103

by: Ohlsson Sax, Olof (Imperial Coll., London) et al.**Abstract:**

In the context of the AdS$_3$/CFT$_2$ correspondence, we investigate the Higgs branch CFT$_2$. Witten showed that states localised near the small instanton singularity can be described in terms of vector multiplet variables. This theory has a planar, weak-coupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin-chain with nearest-neighbour interactions. This CFT$_2$ spin-chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS$_3$ side of the duality. We compute the one-loop dilatation operator in a non-trivial compact subsector and show that it corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT$_2$ side of the correspondence.
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Detailed record: *http://inspirehep.net/record/1327780*