Organized by:
- Ben Hoare (Durham University)
- Charlotte Kristjansen (Niels Bohr Institute)
- Andrew O’Bannon (SUNY Old Westbury)
- Alessandro Sfondrini (Padova University)
- Daniel C. Thompson (Swansea University)
Exactly-solvable models are a cornerstone of theoretical physics: they allow a detailed understanding of new phenomena and provide the starting point for all approximations and numerics. These models have long been believed to be exceedingly rare due to their rich symmetry structure. A cluster of recent discoveries has revolutionized this perspective, exposing a vast web of exactly-solvable models related to each other through integrable deformations and dualities.
These ideas have been especially fruitful in the context of holography. Exact solvability of planar N=4 supersymmetric Yang-Mills theory has given us an unprecedented ability to interpolate between weak and strong coupling, not only in the case of the spectrum of non-protected local operators of the theory but also for quantities such as the qq-potential and the Hagedorn temperature of the dual string theory. These achievements might have appeared to be tied to the rather rigid and highly (super)symmetric nature of that AdS/CFT set-up. Yet, over the last few years we are coming to understand that many of those integrable
structures can be deformed and generalized, often yielding multi-parametric integrable models. The major avenues of exploration in this context are:
1. The inclusion of boundaries and defects, such as domain walls, Wilson or ‘t Hooft lines (branes, in the string picture) which break supersymmetry, partially or completely, but leave a sufficient amount of symmetry to exactly determine e.g. one-point functions. Work in vector models and in Chern-Simons matter theories have catalysed progress in providing a full quantum evaluation of defects.
2. The study of lower-dimensional AdS/CFT setups, where the maximal amount of supersymmetry is limited, and more parameters naturally play a
role, with the possibility of interpolating between superstring backgrounds of Wess-Zumino-Novikov-Witten type and those supported by Ramond-Ramond fluxes. Important lessons for these setups have also come from progress constructing the gravitational duals of gauge theories at zero coupling.
3. The study of integrable deformations of (superstring) sigma models, which over the last few years has been made systematic within the language of Yang-Baxter deformations, Poisson-Lie T-dualities and higher-dimensional Chern-Simons theories. These are supplemented with a remarkable universal class of TTbar deformations with exciting applications to holography.
