Exact Chern-Simons / Topological String duality

Krefl, Daniel; Mkrtchyan, R. L.

doi:10.48550/arxiv.1506.03907

Cited by 14 publications

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“…This program is successful for Chern-Simons theory on the 3d sphere [1,2], and has led to establishment of exact (i.e. non-perturbative) Chern-Simons/topological strings duality for SU(N) gauge groups [6], similar results in refined cases [6], gauge/string duality conjecture for exceptional groups [23], universal knot polynomials [3], and other achievements.…”

Section: Discussionmentioning

confidence: 99%

“…[1,2] for universal expression for partition function and [3,4] for universal knot polynomials (Wilson loops). Universal formulae appear to be relevant also for refined Chern-Simons theory [5], non-perturbative gauge/string duality [6] and Diophantine classification of simple Lie algebras [7,8]. Universality approach reveals [9] details of behavior of SU (N ) Chern-Simons partition function under N → −N duality, and, more generally, under permutations of universal parameters (Vogel's symmetry).…”

Section: Introductionmentioning

confidence: 99%

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On universal quantum dimensions

Mkrtchyan

2017

Nuclear Physics B

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We represent in the universal form restricted one-instanton partition function of supersymmetric Yang-Mills theory. It is based on the derivation of universal expressions for quantum dimensions (universal characters) of Cartan powers of adjoint and some other series of irreps of simple Lie algebras. These formulae also provide a proof of formulae for universal quantum dimensions for low-dimensional representations, needed in derivation of universal knot polynomials (i.e. colored Wilson averages of Chern-Simons theory on 3d sphere). As a check of the (complicated) formulae for universal quantum dimensions we prove numerically Deligne's hypothesis on universal characters for symmetric cube of adjoint representation.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On universal quantum dimensions

Mkrtchyan

2017

Nuclear Physics B

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“…Dimension formulae are given in [1,15,3]. Universal formulae were derived for compact groups volume [16,17] and for the anomaly of Vogel's permutation symmetry [17]. Universal formulae were discovered in applications, mainly in Chern-Simons theory: partition function [18,5], knot polynomials (Wilson loops) [19], central charge, etc.…”

Section: Appendix a Vogel's Parametersmentioning

confidence: 99%

On universal quantum dimensions of certain two-parameter series of representations

Avetisyan,

Mkrtchyan

2019

Preprint

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We present the universal, in Vogel's sense, expression for the quantum dimension of Cartan product of an arbitrary number of adjoint and X2 representations of simple Lie algebras. The same formula mysteriously gives quantum dimensions of some other representations of the same Lie algebra under permutations of universal parameters. We list these representations for exceptional algebras and stable versions for classical algebras, when the rank of the classical algebra is sufficiently large w.r.t. the powers of representations. We show that universal formulae can have singularities on Vogel's plane for some algebras, and that they give correct answers when restricted on appropriate lines on Vogel's plane. We note that the same irreducible representation can have several universal formulae for its (quantum) dimension, and discuss the implication of this phenomena on the Cohen -de Man method of calculation of universal formulae.

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“…The main features of representation of partition function discovered in [2,3] has been extended to include the partition function of the refined Chern-Simons theory S 3 sphere 1 for An and Dn algebras in [11]. It has also been shown to be very convenient for derivation of the partition function of dual refined topological strings in [12]. In the same work the non-perturbative corrections to the partition function of topological strings, derived from the universal Chern-Simons partition function [3] (with An gauge algebra), has been shown to coincide with those, derived in [13,14] directly in topological string theory, thus extending the CS/topological strings duality to the non-perturbative domain.…”

Section: Introductionmentioning

confidence: 99%

On partition functions of refined Chern-Simons theories on $S^3$

Avetisyan¹,

Mkrtchyan²

2021

Preprint

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We present a new expression for the partition function of refined Chern-Simons theory on S 3 with arbitrary gauge group, which is explicitly equal to 1, when the coupling constant is zero. Using this form of partition function we show that the previously known Krefl-Schwarz representation of partition function of refined Chern-Simons theory on S 3 can be generalized to all simply-laced algebras.For all non-simply-laced gauge algebras we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of a duality with refined topological strings.

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Exact Chern-Simons / Topological String duality

Cited by 14 publications

References 0 publications

On universal quantum dimensions

On universal quantum dimensions

On universal quantum dimensions of certain two-parameter series of representations

On partition functions of refined Chern-Simons theories on $S^3$

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