标题： 从质量变形的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) x U(N+M) ABJM理论的分划函数满足一组双线性关系，这些关系在广义分划函数中被发现是q-Painleve III_3方程。 在本文中，我们提出对于一个任意复数值的质量参数，保持N=6的质量变形的ABJM理论也存在类似的双线性关系，我们通过使用不同N,k,M和质量参数的分划函数的精确值提供了几个非平凡的验证。 对于由整数标记的质量参数$\nu,a$作为$m_1=m_2=-\pi i(\nu-2a)/\nu$，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 was 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.