标题： 从质量形变的ABJM理论中得到的SU(N) q-Toda方程 显示英文标题

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

摘要： 已知U(N) × U(N+M) ABJM理论的配分函数满足一组双线性关系，将其写为巨配分函数时，最近发现该关系对应于q-Painlevé III_3方程。 本文提出了一种类似的双线性关系，适用于具有任意复数量纲参数的N=6质量变形保持的ABJM理论，并通过使用各种N、k、M和量纲参数的确切配分函数值提供了多个非平凡检验。 对于由整数标记的质量参数的特定选择$\nu,a$对应$m_1=m_2=-\pi i(\nu-2a)/\nu$时，双线性关系对应于$\tau$形式的仿射SU($\nu$) Toda方程的q变形。 显示英文摘要

摘要： 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.