# Integrability in Gauge and String Theory 2013

**Conference on Integrability in Gauge and String Theory in Utrecht**

*Over 150 researcher joined the workshop*

From 19 to 23 August 2013 the yearly conference on Integrability in Gauge and String Theory (IGST 2013) took place in Utrecht. The primary goal of this workshop was to survey the most recent progress in the field. This, which was fully achieved. It furthermore provided a forum for the discussion of open problems and inspired active interactions between researchers on quantum field theory, string theorists, condensed matter physicists and mathematicians.

About 150 researcher joined the workshop, including a large number of students and postdocs, many of which were able to join because of GATIS funding. Numerous young researchers presented and discussed their work in the accompanying poster session. Prominent speakers, many of them also at an early stage of their career, presented the latest advances in this fast-moving field. The conference was perfectly organized by Gleb Arutyunov with crucial help by Bernard de Wit, Stefan Vandoren, and the managing director Joost van Zee, as well as their young team of helpers Riccardo Borsato, Alessandro Sfondrini, and Stijn van Tongeren.

The correspondence between gauge and string theories offers an entirely new way to explore fundamental interactions of matter. In recent years remarkable progress has been made towards a quantitative understanding of this correspondence based on ideas of exact integrability. Integrable models constitute a special class of dynamical systems with unusually many conservation laws, that in many cases hold the key to their exact solution. This circle of ideas is explored in an annual workshop series. This year it took place at the University of Utrecht, surveying the most recent progress in this field.

One highlight was the calculation of the so-called Konishi anomalous dimension of N=4 gauge theory to nine orders in the Feynman loop expansion, using a quantum spectral curve as presented by Dmytro Volin and Nikolay Gromov. The latest progress on the thermodynamic Bethe ansatz approach was discussed in Zoltan Bajnok's talk on brane-anti-brane systems, and in Roberto Tateo’s talk on the quark-antiquark potential. A systematic strategy to get deeper into the algebraic structure of the AdS/CFT system was proposed in Marius de Leeuw’s talk on the Yangian algebra. An intriguing physical approach to deeper explore the integrable structure of the system was presented by Gregory Korchemsky. Jan Plefka discussed the Yangian of Wilson loops and Rouven Frassek a systematic way to construct Yangian invariants using the Bethe ansatz. Jaroslav Trnka presented the latest work on the all-loop integrand of the N = 4 scattering amplitudes. An interesting open challenge is to relate this approach to integrability, and to reproduce the so-called exact cusp equation.

There were also interesting talks by Luigi Cantini on combinatorics and integrability, by Matthias Gaberdiel on minimal model holography, and by Paul Pearce on logarithmic minimal models. Vasily Pestun spoke on the relation between the partition function of quiver gauge theories and integrable systems. Progress on fascinating lower dimensional “relatives” of the AdS/CFT system was reported by Olof Ohlsson Sax, Radu Roiban, and Arkady Tseytlin. Intriguing surprises and puzzles of deformations of the N=4 field theory which were conjectured to be integrable emerged in the presentation of Christoph Sieg. High energy scattering and the BFKL equation remain an interesting challenge for integrability. We heard about promising advances from Romuald Janik and from Nikolay Gromov. There is stunning progress using integrability in the context of the amplitudes/Wilson loop duality, as was reported by Benjamin Basso and by Pedro Vieira. There also continues to be steady progress in the difficult problem of correlation functions, see the talks by Agnese Bissi and by Ivan Kostov, and on form factors, of the presentation of Tristan McLoughlin.

The programme and the talks are available on the conference webpage:

http://testweb.science.uu.nl/IGST13/files/program.html