Contributor info: Dr Piotr Sulkowski

Aditya Bawane, Pedram Karimi, Piotr Sułkowski

SciPost Phys. 13, 069 (2022) · published 27 September 2022 | Toggle abstract · pdf

In this note we provide proofs of various expressions for expectation values of symmetric polynomials in $\beta$-deformed eigenvalue models with quadratic, linear, and logarithmic potentials. The relations we derive are also referred to as superintegrability. Our work completes proofs of superintegrability statements conjectured earlier in literature.

Taro Kimura, Miłosz Panfil, Yuji Sugimoto, Piotr Sułkowski

SciPost Phys. 10, 051 (2021) · published 26 February 2021 | Toggle abstract · pdf

We consider a large class of branes in toric strip geometries, both non-periodic and periodic ones. For a fixed background geometry we show that partition functions for such branes can be reinterpreted, on one hand, as quiver generating series, and on the other hand as wave-functions in various polarizations. We determine operations on quivers, as well as $SL(2,\mathbb{Z})$ transformations, which correspond to changing positions of these branes. Our results prove integrality of BPS multiplicities associated to this class of branes, reveal how they transform under changes of polarization, and imply all other properties of brane amplitudes that follow from the relation to quivers.