Z-extremization and F-theorem in Chern-Simons matter theories
arXiv:1105.0933 · doi:10.1007/JHEP10(2011)016
Abstract
The three dimensional exact R symmetry of N=2 SCFTs extremizes the partition function localized on a three sphere. Here we verify this statement at weak coupling. We give a detailed analysis for two classes of models. The first one is an SU(N)_k gauge theory at large k with both fundamental and adjoint matter fields, while the second is a flavored version of the ABJ theory, where the CS levels are large but they do not necessarily sum up to zero. We study in both cases superpotential deformations and compute the R charges at different fixed points. When these fixed points are connected by an RG flow we explicitly verify that the free energy decreases at the endpoints of the flow between the fixed points, corroborating the conjecture of an F-theorem in three dimensions.
28 pages, 3 figures, JHEP.cls, minor corrections, references added
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- Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors
- The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
- Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories
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- A Crack in the Conformal Window
- Free Energy of D_n Quiver Chern-Simons Theories
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- Refined Checks and Exact Dualities in Three Dimensions
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- Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
- Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
- On the Higgsing and UnHiggsing of Fano 3-Folds
- Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and oscillators