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SU(N) q-Toda equations from mass deformed ABJM theory
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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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Cited by 1 Pith paper
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Five-brane webs, 3d $\mathcal{N}=2$ theories and quantum curves
The Newton polygon of the quantum curve for a 3d N=2 brane configuration is conjectured to equal the toric diagram dual to its (p,q) 5-brane web, with derivations for Lagrangian cases and new matrix models for p>=2.
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