(Ir)regular singularities and Quantum Field Theory

PUBLICATIONS

| Random Matrices and Gauge theories

Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory

Author(s)

Leonardo Santilli and Miguel Tierz

Topic

Random Matrices and Gauge theories

Abstract

We study the phase transitions of three-dimensional =2 U(N) Chern-Simons theory on 𝕊3 with a varied number of massive fundamental hypermultiplets and with a Fayet-Iliopoulos parameter. We characterize the various phase diagrams in the decompactification limit, according to the number of different mass scales in the theory. For this, we extend the known solution of the saddle-point equations to the setting where the one cut solution is characterized by asymmetric intervals. We then study the large N limit of Wilson loops in antisymmetric representations, with the additional scaling corresponding to the variation of the size of the representation. We give explicit expressions, both with and without FI terms, and study 1/R corrections for the different phases. These corrections break the perimeter law behavior, as they introduce a scaling with the size of the representation. We show how the phase transitions of the Wilson loops can either be of first or second order and determine the underlying mechanism in terms of the eventual asymmetry of the support of the solution of the saddle-point equation, at the critical points.

Year

2019

Reference

L. Santilli and M. Tierz, “Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory,” J. Phys. A 52, no. 38, 385401 (2019).

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