Crossing symmetry in the planar limit

Sebastian Mizera

doi:10.1103/physrevd.104.045003

Multiple phases in a generalized Gross-Witten-Wadia matrix model

Journal of High Energy Physics ◽

10.1007/jhep09(2020)081 ◽

2020 ◽

Vol 2020 (9) ◽

Cited By ~ 2

Author(s):

Jorge G. Russo ◽

Miguel Tierz

Keyword(s):

Partition Function ◽

Matrix Models ◽

Characteristic Polynomial ◽

Matrix Model ◽

Phase Structure ◽

Unitary Matrix ◽

Two Dimensional ◽

Toeplitz Determinants ◽

Dimensional Parameter ◽

Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

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The planar limit of $$ \mathcal{N} $$ = 2 chiral correlators

Journal of High Energy Physics ◽

10.1007/jhep08(2021)032 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Bartomeu Fiol ◽

Alan Rios Fukelman

Keyword(s):

Free Energy ◽

Infinite Number ◽

Correlation Functions ◽

Hermitian Matrix ◽

Hooft Coupling ◽

Planar Limit ◽

Single Trace ◽

Hermitian Matrix Model ◽

Combinatorial Expression ◽

Do So

Abstract We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of $$ \mathcal{N} $$ N = 2 SQCD on S4, to all orders in the ’t Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ℝ4. Specifically, we compute all the terms with a single value of the ζ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ℝ4.

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Duality and crossing symmetry of the narrow resonance model

Canadian Journal of Physics ◽

10.1139/p70-179 ◽

1970 ◽

Vol 48 (12) ◽

pp. 1426-1429 ◽

Cited By ~ 1

Author(s):

K. Nakazawa

Keyword(s):

Finite Energy ◽

Complex Variables ◽

Narrow Resonance ◽

Veneziano Amplitude ◽

Resonance Model ◽

Sum Rule ◽

Crossing Symmetry ◽

The One

In the narrow resonance approximation, conditions of duality and crossing symmetry are derived using the finite energy sum rule for an amplitude which is completely determined as a function of two complex variables by its meromorphic part in one of these variables. As an example, the one term Veneziano amplitude is discussed.

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