Z Extremization in Chiral-Like Chern Simons Theories

Abstract

We study the localized free energy on S^3 of three-dimensional N=2 Chern-Simons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by applying the standard saddle point approximation for large N. We show that the latter approach does not reproduce the expected result when chiral theories are considered. We circumvent these problems by restoring a reflection symmetry on the eigenvalues in the free energy. Thanks to this symmetrization we find that the three methods employed agree. In particular we match the computation for a model whose four dimensional parent is the quiver gauge theory describing D3 branes probing the Hirzebruch surface. We conclude by commenting on the application of our results and to the strong coupling regime.

20 pages, 1 figure, using jheppub.sty

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• Geometry of $\mathcal{I}$-extremization and black holes microstates
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• Sphere correlation functions and Verma modules
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• Refined Checks and Exact Dualities in Three Dimensions
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Tests of AdS${}_4$/CFT${}_3$ correspondence for $\mathcal{N}=2$ chiral-like theory
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• Is toric duality a Seiberg-like duality in (2+1)-d ?
• Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories