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Partition functions of 3d \( \widehat{D} \)-quivers and their mirror duals from 1d free fermions

  • Benjamin AsselEmail author
  • Nadav Drukker
  • Jan Felix
Open Access
Regular Article - Theoretical Physics

Abstract

We study the matrix models calculating the sphere partition functions of 3d gauge theories with \( \mathcal{N}=4 \) supersymmetry and a quiver structure of a \( \widehat{D} \) Dynkin diagram (where each node is a unitary gauge group). As in the case of necklace (Â) quivers, we can map the problem to that of free fermion quantum mechanics whose complicated Hamiltonian we find explicitly. Many of these theories are conjectured to be dual under mirror symmetry to certain unitary linear quivers with extra Sp nodes or antisymmetric hypermultiplets. We show that the free fermion formulation of such mirror pairs are related by a linear symplectic transformation.

We then study the large N expansion of the partition function, which as in the case of the  quivers is given to all orders in 1/N by an Airy function. We simplify the algorithm to calculate the numerical coefficients appearing in the Airy function and evaluate them for a wide class of \( \widehat{D} \)-quiver theories.

Keywords

Matrix Models Supersymmetry and Duality Field Theories in Lower Dimensions Duality in Gauge Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonLondonUnited Kingdom

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