Superintegrability summary

Миронов, А.; Морозов, А.

doi:10.1016/j.physletb.2022.137573

Cited by 30 publications

(7 citation statements)

References 35 publications

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“…The CTST algorithms of the present paper, which are based on matrix equations, would similarly be amenable to quantum algorithms. Finite groups arise as hidden symmetries in correlator computations for matrix and tensor models (see for example recent work [49,50]) with continuous group gauge symmetries. This gives an avenue for wider applications in holography and gauge-string duality for algorithms related to finite group representation theory.…”

Section: Discussionmentioning

confidence: 99%

Row–column duality and combinatorial topological strings

Padellaro,

Radhakrishnan,

Ramgoolam

2024

J. Phys. A: Math. Theor.

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Integrality properties of partial sums over irreducible representations, along columns of character tables of finite groups, were recently derived using combinatorial topological string theories (CTST). These CTST were based on Dijkgraaf-Witten theories of flat G-bundles for finite groups G in two dimensions, denoted G-TQFTs. We define analogous combinatorial topological strings related to two dimensional TQFTs based on fusion coefficients of finite groups. These TQFTs are denoted as R(G)-TQFTs and allow analogous integrality results to be derived for partial row sums of characters over conjugacy classes along fixed rows. This relation between the G-TQFTs and R(G)-TQFTs defines a row-column duality for character tables, which provides a physical framework for exploring the mathematical analogies between rows and columns of character tables. These constructive proofs of integrality are complemented with the proof of similar and complementary results using the more traditional Galois theoretic framework for integrality properties of character tables. The partial row and column sums are used to define generalised partitions of the integer row and column sums, which are of interest in combinatorial representation theory.

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Section: Discussionmentioning

confidence: 99%

Row–column duality and combinatorial topological strings

Padellaro,

Radhakrishnan,

Ramgoolam

2024

J. Phys. A: Math. Theor.

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“…Superintegrability. Equations (4.5), (4.7), and (4.9) can be interpreted as examples of the of matrix model superintegrability [MM22], namely for ℓ(λ) ≤ N the integrals of the Schur functions are proportional to the same Schur functions:…”

Section: 2mentioning

confidence: 99%

Generalized Brézin–Gross–Witten tau-function as a hypergeometric solution of the BKP hierarchy

Alexandrov

2023

Advances in Mathematics

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“…which is a sum over the Schur functions with factorized coefficients proportional to the same Schur functions evaluated at special loci. Such specific form of a sum is nicknamed a superintegrability property [44][45][46].…”

Section: Description Of the Modelmentioning

confidence: 99%

Spectral curves and W-representations of matrix models

Mironov

Морозов

2023

J. High Energ. Phys.

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We explain how the spectral curve can be extracted from the $$ \mathcal{W} $$ W -representation of a matrix model. It emerges from the part of the $$ \mathcal{W} $$ W -operator, which is linear in time-variables. A possibility of extracting the spectral curve in this way is important because there are models where matrix integrals are not yet available, and still they possess all their important features. We apply this reasoning to the family of WLZZ models and discuss additional peculiarities which appear for the non-negative value of the family parameter n, when the model depends on additional couplings (dual times). In this case, the relation between topological and 1/N expansions is broken. On the other hand, all the WLZZ partition functions are τ-functions of the Toda lattice hierarchy, and these models also celebrate the superintegrability properties.

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Superintegrability summary

Cited by 30 publications

References 35 publications

Row–column duality and combinatorial topological strings

Row–column duality and combinatorial topological strings

Generalized Brézin–Gross–Witten tau-function as a hypergeometric solution of the BKP hierarchy

Spectral curves and W-representations of matrix models

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