In this paper we investigate a novel connection between the effective theory of M2-branes on (C-2/Z(2)xC(2)/Z(2))/Z(k) and the q-deformed Painleve 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-Painleve 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-Painleve III3, and topological strings on local P-1 x P-1. From the mathematical viewpoint the quiver Chern-Simons theory provides a conjectural Fredholm determinant realisation of the q-Painleve VI tau-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-Painleve III3.

M2-branes and q-Painlevé equations / Bonelli, G.; Globlek, F.; Kubo, N.; Nosaka, T.; Tanzini, A.. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 112:6(2022), pp. 1-69. [10.1007/s11005-022-01597-0]

M2-branes and q-Painlevé equations

Bonelli, G.;Globlek, F.;Tanzini, A.
2022-01-01

Abstract

In this paper we investigate a novel connection between the effective theory of M2-branes on (C-2/Z(2)xC(2)/Z(2))/Z(k) and the q-deformed Painleve 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-Painleve 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-Painleve III3, and topological strings on local P-1 x P-1. From the mathematical viewpoint the quiver Chern-Simons theory provides a conjectural Fredholm determinant realisation of the q-Painleve VI tau-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-Painleve III3.
2022
112
6
1
69
109
https://doi.org/10.1007/s11005-022-01597-0
Bonelli, G.; Globlek, F.; Kubo, N.; Nosaka, T.; Tanzini, A.
File in questo prodotto:
File Dimensione Formato  
s11005-022-01597-0.pdf

accesso aperto

Licenza: Non specificato
Dimensione 1.19 MB
Formato Adobe PDF
1.19 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/131614
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact