scholarly journals Combinatorics of Bousquet-Mélou–Schaeffer numbers in the light of topological recursion

2020 ◽  
Vol 90 ◽  
pp. 103184
Author(s):  
B. Bychkov ◽  
P. Dunin-Barkowski ◽  
S. Shadrin
Keyword(s):  
Topological Recursion

scholarly journals On topological recursion for Wilson loops in $$ \mathcal{N} $$ = 4 SYM at strong coupling

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
M. Beccaria ◽  
A. Hasan
Keyword(s):  
Strong Coupling ◽  
Matrix Model ◽  
Wilson Loops ◽  
Expectation Value ◽  
Yang Mills ◽  
Usual Procedure ◽  
Topological Recursion ◽  
Sample Application ◽  
Single Trace ◽  
Genus Expansion

Abstract We consider U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling λ, order by order in 1/N, and then taking the λ ≫ 1 limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885.

scholarly journals Combinatorics of KP hierarchy structural constants

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Initial Data ◽  
Integral Representation ◽  
Internal Structure ◽  
Generating Functions ◽  
Transport Coefficients ◽  
Mathematical Physics ◽  
Combinatorial Structure ◽  
Kp Hierarchy ◽  
Topological Recursion ◽  
Structure Research

AbstractWe investigate the structural constants of the KP hierarchy, which appear as universal coefficients in the paper of Natanzon–Zabrodin arXiv:1509.04472. It turns out that these constants have a combinatorial description in terms of transport coefficients in the theory of flow networks. Considering its properties we want to point out three novel directions of KP combinatorial structure research: connection with topological recursion, eigenvalue model for the structural constants and its deformations, possible deformations of KP hierarchy in terms of the structural constants. Firstly, in this paper we study the internal structure of these coefficients which involves: (1) construction of generating functions that have interesting properties by themselves; (2) restrictions on topological recursion initial data; (3) construction of integral representation or matrix model for these coefficients with non-trivial Ward identities. This shows that these coefficients appear in various problems of mathematical physics, which increases their value and significance. Secondly, we discuss their role in integrability of KP hierarchy considering possible deformation of these coefficients without changing the equations on $$\tau $$ τ -function. We consider several plausible deformations. While most failed even very basic checks, one deformation (involving Macdonald polynomials) passes all the simple checks and requires more thorough study.

scholarly journals Voros coefficients for the hypergeometric differential equations and Eynard–Orantin’s topological recursion: Part II: For confluent family of hypergeometric equations

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Kohei Iwaki ◽  
Tatsuya Koike ◽  
Yumiko Takei
Keyword(s):  
Free Energy ◽  
Differential Equations ◽  
Classical Limit ◽  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Spectral Curves ◽  
Topological Recursion ◽  
Hypergeometric Equations ◽  
Explicit Expressions

Abstract We show that each member of the confluent family of the Gauss hypergeometric equations is realized as quantum curves for appropriate spectral curves. As an application, relations between the Voros coefficients of those equations and the free energy of their classical limit computed by the topological recursion are established. We will also find explicit expressions of the free energy and the Voros coefficients in terms of the Bernoulli numbers and Bernoulli polynomials. Communicated by: Youjin Zhang

scholarly journals Weighted Hurwitz Numbers and Topological Recursion

2020 ◽  
Vol 375 (1) ◽  
pp. 237-305 ◽  
Author(s):  
A. Alexandrov ◽  
G. Chapuy ◽  
B. Eynard ◽  
J. Harnad
Keyword(s):  
Hurwitz Numbers ◽  
Topological Recursion

scholarly journals Weighted Hurwitz numbers and topological recursion: An overview

2018 ◽  
Vol 59 (8) ◽  
pp. 081102 ◽  
Author(s):  
A. Alexandrov ◽  
G. Chapuy ◽  
B. Eynard ◽  
J. Harnad
Keyword(s):  
Hurwitz Numbers ◽  
Topological Recursion

scholarly journals Super Quantum Airy Structures

2020 ◽  
Vol 380 (1) ◽  
pp. 449-522
Author(s):  
Vincent Bouchard ◽  
Paweł Ciosmak ◽  
Leszek Hadasz ◽  
Kento Osuga ◽  
Błażej Ruba ◽  
...  
Keyword(s):  
Classification Scheme ◽  
Graphical Representation ◽  
Free Energies ◽  
Recursion Relations ◽  
Gauge Transformations ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Frobenius Algebras ◽  
Topological Recursion

Abstract We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations. Furthermore, we present various examples of super quantum Airy structures, both finite-dimensional—which include well known superalgebras and super Frobenius algebras, and whose classification scheme we also discuss—as well as infinite-dimensional, that arise in the realm of vertex operator super algebras.

scholarly journals Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

2017 ◽  
Vol 360 (2) ◽  
pp. 777-826 ◽  
Author(s):  
A. Alexandrov ◽  
G. Chapuy ◽  
B. Eynard ◽  
J. Harnad
Keyword(s):  
Hurwitz Numbers ◽  
Topological Recursion
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