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arXiv · 2012.07211

SU(N) q-Toda equations from mass deformed ABJM theory

Tomoki Nosaka
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Abstract

It is known that the partition functions of the U(N) x U(N+M) ABJM theory satisfy a set of bilinear relations, which, written in the grand partition function, was recently found to be the q-Painleve III_3 equation. In this paper we have suggested a similar bilinear relation holds for the ABJM theory with N=6 preserving mass deformation for an arbitrary complex value of mass parameter, to which we have provided several non-trivial checks by using the exact values of the partition functions for various N,k,M and the mass parameter. For particular choices of the mass parameters labeled by integers $\nu,a$ as $m_1=m_2=-\pi i(\nu-2a)/\nu$, the bilinear relation corresponds to the q-deformation of the affine SU($\nu$) Toda equation in $\tau$-form.

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Tomoki Nosaka. 2020-12-14. SU(N) q-Toda equations from mass deformed ABJM theory. https://doi.org/10.1007/jhep06(2021)060

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