• Corpus ID: 245650290

# Integrability from supersymmetric duality: a short review

@inproceedings{Gahramanov2022IntegrabilityFS,
title={Integrability from supersymmetric duality: a short review},
author={Ilmar Gahramanov},
year={2022}
}
Integrable models of statistical mechanics play a prominent role in modern mathematical physics, especially in conformal field theory, knot theory, combinatorics, topology, etc. In this brief review, we discuss a program of constructing integrable lattice spin models with the nearest neighbor interaction using methods inspired by the supersymmetric gauge theory computations, called gauge/YBE correspondence. After a brief introduction to the topic, we review some recent examples of this…
2 Citations

## Figures from this paper

Lens Partition Functions and Integrability Properties
• Physics, Mathematics
• 2021
Abstract: We study lens partitions functions for the three-dimensional N = 2 supersymmetric gauge theories on S3 b /Zr. We consider equality as a new hyperbolic hypergeometric solution to the
A comment on the solutions of the generalized Faddeev-Volkov model
: We consider two recent generalizations of the Faddeev-Volkov model, which is exactly solvable Ising-type lattice spin model. The ﬁrst generalization based on using of the non-compact quantum

## References

SHOWING 1-10 OF 98 REFERENCES
Integrable Lattice Spin Models from Supersymmetric Dualities
• Physics, Mathematics
Physics of Particles and Nuclei Letters
• 2018
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that
Superconformal indices, dualities and integrability
In this thesis we discuss exact, non-perturbative results achieved using superconformal index technique in supersymmetric gauge theories with four supercharges (which is N = 1 supersymmetry in four
SUPERCONFORMAL INDICES AND PARTITION FUNCTIONS FOR SUPERSYMMETRIC FIELD THEORIES
• Physics
• 2013
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of
Yang-Baxter equation in integrable systems
This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S
Superconformal Indices, Seiberg Dualities and Special Functions
This is a brief account of relations between the theory of special functions, on the one side, and superconformal indices and Seiberg dualities of four-dimensional $\mathcal{N}=1$ supersymmetric
Calculating the Superconformal Index and Seiberg Duality
We develop techniques to calculate an index for four dimensional superconformal field theories. This superconformal index is counting BPS operators which preserve only one supercharge. To calculate
An introduction to localisation and supersymmetry in curved space.
This paper presents the lecture notes of a course that I taught at the Ninth Modave Summer School in Mathematical Physics. The course has been designed to give an introduction to new exact results
Elliptic beta integrals and solvable models of statistical mechanics
The univariate elliptic beta integral was discovered by the author in 2000. Recently Bazhanov and Sergeev have interpreted it as a star-triangle relation (STR). This important observation is