Bilinear character correlators in superintegrable theory

Mironov, A.; Morozov, A.

doi:10.48550/arxiv.2206.02045

Cited by 4 publications

(8 citation statements)

References 23 publications

(35 reference statements)

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“…In this section, we demonstrate that superintegrability implies a factorization of proper double correlators of the Schur functions, which allows one to rewrite (15) as an explicit series with coefficients being the standard Nekrasov functions.…”

Section: Factorization Of Double Correlatorsmentioning

confidence: 90%

“…The Kadell formulas, however, demonstrate that, for a particular double-logarithmic Dotsenko-Fateev matrix model [8,14], they do, at expense of a simple pointsplitting by v in (1). This is a drastic simplification as compared to the recently analyzed Gaussian Hermitian model where certain bilinear combinations of characters were also shown to factorize [15], but the simple pointsplitting interpretation is not available.…”

Section: Introductionmentioning

confidence: 85%

“…In fact, there are bilinears in the Gaussian model, which are factorized, but they are more complicated [15] (see sec.5.2). Thus bilinear factorization has a chance to be a generically present enhancement and even corollary of superintegrability, but only in the Selberg case it is described by a point-splitting.…”

Section: Factorization Property Of Double Correlatorsmentioning

confidence: 99%

“…where µ R,∆ are numbers that do not depend on the size of matrix N , see [15] for details. In this formula, P is even, since otherwise both the average of S R vanishes and µ R,∆ becomes singular.…”

Section: Model With Gaussian DV Building Blocksmentioning

confidence: 99%

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Superintegrability as the hidden origin of Nekrasov calculus

Mironov¹,

Morozov²

2022

Preprint

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Once famous and a little mysterious, AGT relations between Nekrasov functions and conformal blocks are now understood as the Hubbard-Stratanovich duality in the Dijkgraaf-Vafa (DV) phase of a peculiar Dotsenko-Fateev multi-logarithmic matrix model. However, it largely remains a collection of somewhat technical tricks, lacking a clear and generalizable conceptual interpretation. Our new claim is that the Nekrasov functions emerge in matrix models as a straightforward implication of superintegrability, factorization of peculiar matrix model averages. Recently, we demonstrated that, in the Gaussian Hermitian model, the factorization property can be extended from averages of single characters to their bilinear combinations. In this paper, we claim that this is true also for multi-logarithmic matrix models, where factorized are just the point-split products of two characters. It is this enhanced superintegrability that is responsible for existence of the Nekrasov functions and the AGT relations. This property can be generalized both to multimatrix models, thus leading to AGT relations for multi-point conformal blocks, and to DV phases of other non-Gaussian models.

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Section: Factorization Of Double Correlatorsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 85%

Section: Factorization Property Of Double Correlatorsmentioning

confidence: 99%

Section: Model With Gaussian DV Building Blocksmentioning

confidence: 99%

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Superintegrability as the hidden origin of Nekrasov calculus

Mironov¹,

Morozov²

2022

Preprint

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“…Recently there has been increasing interest in the superintegrability for matrix models [1]- [18]. The superintegrability means that for the character expansions of the matrix models, the average of a properly chosen symmetric function is proportional to ratios of symmetric functions on a proper locus, i.e., < character >∼ character.…”

Section: Introductionmentioning

confidence: 99%

Superintegrability for ($β$-deformed) partition function hierarchies with $W$-representations

Wang¹,

Liu²,

Zhang³

et al. 2022

Preprint

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We construct the (β-deformed) partition function hierarchies with W -representations. Based on the W -representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and Jack polynomials, respectively. Some well known superintegrable matrix models such as the Gaussian hermitian one-matrix model (in the external field), N × N complex matrix model, β-deformed Gaussian hermitian and rectangular complex matrix models are contained in the constructed hierarchies.

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Superintegrability for ($$\beta $$-deformed) partition function hierarchies with W-representations

et al. 2022

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We construct the ($$\beta $$ β -deformed) partition function hierarchies with W-representations. Based on the W-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and Jack polynomials, respectively. Some well known superintegrable matrix models such as the Gaussian hermitian one-matrix model (in the external field), $$N\times N$$ N × N complex matrix model, $$\beta $$ β -deformed Gaussian hermitian and rectangular complex matrix models are contained in the constructed hierarchies.

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Bilinear character correlators in superintegrable theory

Cited by 4 publications

References 23 publications

Superintegrability as the hidden origin of Nekrasov calculus

Superintegrability as the hidden origin of Nekrasov calculus

Superintegrability for ($β$-deformed) partition function hierarchies with $W$-representations

Superintegrability for ($$\beta $$-deformed) partition function hierarchies with W-representations

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