M2-branes and $\mathfrak{q}$-Painlevé equations

Bonelli, Giulio; Globlek, Fran; Kubo, Naotaka; Nosaka, Tomoki; Tanzini, Alessandro

doi:10.48550/arxiv.2202.10654

Cited by 3 publications

(3 citation statements)

References 76 publications

(152 reference statements)

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“…It is important to elaborate the relations especially from integrabilities [58][59][60][61][62][63][64]. Sixthly, we have studied the relations between duality cascades and parallelotopes mainly having the setup of three-dimensional supersymmetric Chern-Simons theories in mind.…”

Section: Discussionmentioning

confidence: 99%

Duality cascades and parallelotopes

Furukawa¹,

Moriyama²,

Sasaki³

2023

J. Phys. A: Math. Theor.

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Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany-Witten transitions in brane configurations on a circle. In the setup of the ABJM theory and its generalizations, from the physical requirement that duality cascades always end and the final destination depends only on the initial brane configuration, we propose that the fundamental domain of supersymmetric brane configurations in duality cascades can tile the whole parameter space of relative ranks by translations, hence is a parallelotope. We provide our arguments for the proposal.

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Section: Discussionmentioning

confidence: 99%

Duality cascades and parallelotopes

Furukawa¹,

Moriyama²,

Sasaki³

2023

J. Phys. A: Math. Theor.

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show abstract

“…It is important to elaborate the relations especially from integrabilities [45][46][47][48][49][50][51].…”

Section: Discussionmentioning

confidence: 99%

Duality Cascades and Parallelotopes

Furukawa¹,

Moriyama²,

Sasaki³

2022

Preprint

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Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany-Witten transitions in brane configurations on a circle. From the physical requirement that duality cascades always end and the final destination depends only on the initial brane configuration, we propose that the fundamental domain of supersymmetric brane configurations in duality cascades can tile the whole parameter space of relative ranks by translations, hence is a parallelotope. We provide our arguments for the proposal.

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“…It should be possible to apply the approach proposed here to general class-S theories [12] by studying the related isomonodromic deformation problem, for example for circular quivers, generalizing to other classical groups the results of [16,17]. It would be also interesting to extend the analysis to non-self-dual Ω-background, which should amount to the quantization of the τ -systems, and its lift to five-dimensional gauge theories on R 4 × S 1 , which should correspond to quantum q-difference τ -systems [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

tt∗ Toda equations for surface defects in SYM and instanton counting for classical Lie groups

Bonelli¹,

Globlek²,

Tanzini³

2022

J. Phys. A: Math. Theor.

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The partition function of N = 2 super Yang-Mills theories with arbitrary simple gauge group coupled to a self-dual Ω-background is shown to be fully determined by studying the renormalization group equations relevant to the surface operators generating its one-form symmetries. The corresponding system of equations results in a non-autonomous Toda chain on the root system of the Langlands dual, the evolution parameter being the RG scale. A systematic algorithm computing the full multi-instanton corrections is derived in terms of recursion relations whose gauge theoretical solution is obtained just by ﬁxing the perturbative part of the IR prepotential as its asymptotic boundary condition for the RGE. We analyse the explicit solutions of the τ-system for all the classical groups at the diverse levels, extend our analysis to aﬃne twisted Lie algebras and provide conjectural bilinear relations for the τ-functions of linear quiver gauge theory.

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M2-branes and $\mathfrak{q}$-Painlevé equations

Cited by 3 publications

References 76 publications

Duality cascades and parallelotopes

Duality cascades and parallelotopes

Duality Cascades and Parallelotopes

tt∗ Toda equations for surface defects in SYM and instanton counting for classical Lie groups

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