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- Title
M2-branes and q-Painlevé equations.
- Authors
Bonelli, Giulio; Globlek, Fran; Kubo, Naotaka; Nosaka, Tomoki; Tanzini, Alessandro
- Abstract
In this paper we investigate a novel connection between the effective theory of M2-branes on (C 2 / Z 2 × C 2 / Z 2) / Z k and the q -deformed Painlevé equations, by proposing that the grand canonical partition function of the corresponding four-nodes circular quiver N = 4 Chern–Simons matter theory solves the q -Painlevé VI equation. We analyse how this describes the moduli space of the topological string on local dP 5 and, via geometric engineering, five dimensional N f = 4 SU (2) N = 1 gauge theory on a circle. The results we find extend the known relation between ABJM theory, q -Painlevé III 3 , and topological strings on local P 1 × P 1 . From the mathematical viewpoint the quiver Chern–Simons theory provides a conjectural Fredholm determinant realisation of the q -Painlevé VI τ -function. We provide evidence for this proposal by analytic and numerical checks and discuss in detail the successive decoupling limits down to N f = 0 , corresponding to q -Painlevé III 3 .
- Subjects
CHERN-Simons gauge theory; PAINLEVE equations; BRANES; PARTITION functions; TOPOLOGICAL spaces; EQUATIONS; CIRCLE
- Publication
Letters in Mathematical Physics, 2022, Vol 112, Issue 6, p1
- ISSN
0377-9017
- Publication type
Article
- DOI
10.1007/s11005-022-01597-0