On RG Flow of tau_{RR} for Supersymmetric Field Theories in Three-Dimensions

Abstract

The coefficient tau_{RR} of the two-point function of the superconformal U(1)_R currents of N=2 SCFTs in three-dimensions is recently shown to be obtained by differentiating the partition function on a squashed three-sphere with respect to the squashing parameter. With this method, we compute the tau_{RR} for N=2 Wess-Zumino models and SQCD numerically for small number of flavors and analytically in the large number limit. We study the behavior of tau_{RR} under an RG flow by adding superpotentials to the theories. While the tau_{RR} decreases for the gauge theories, we find an N=2 Wess-Zumino model whose tau_{RR} increases along the RG flow. Since tau_{RR} is proportional to the coefficient C_T of the two-point correlation function of the stress-energy tensors for N=2 superconformal field theories, this rules out the possibility of C_T being a measure of the degrees of freedom which monotonically decreases along RG flows in three-dimensions.

24 pages, 4 figures

References in corpus (6)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Notes on SUSY Gauge Theories on Three-Sphere
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• Supersymmetric Field Theories on Three-Manifolds
• Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?

Cited by in corpus (42)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Entanglement entropy: holography and renormalization group
• Universality of corner entanglement in conformal field theories
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Bootstrapping SCFTs with Four Supercharges
• Supersymmetric Renyi Entropy
• Entanglement entropy across a deformed sphere
• Corner contributions to holographic entanglement entropy
• Emergence of supersymmetric quantum electrodynamics
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• Holographic studies of Einsteinian cubic gravity
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• On $C_J$ and $C_T$ in Conformal QED
• Decoding a Three-Dimensional Conformal Manifold
• Optical conductivity of topological surface states with emergent supersymmetry
• Accidental Symmetries and the Conformal Bootstrap
• The F-Theorem and F-Maximization
• On $C_J$ and $C_T$ in the Gross-Neveu and $O(N)$ Models
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Comments on Squashed-sphere Partition Functions
• The NUTs and Bolts of Squashed Holography
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• A search for minimal 4d N=1 SCFT
• Renormalized Entanglement Entropy Flow in Mass-deformed ABJM Theory
• Holographic Entanglement Entropy of Mass-deformed ABJM Theory
• A 3d disordered superconformal fixed point
• Yukawa CFTs and Emergent Supersymmetry
• Supersymmetric dS/CFT
• Evidence for a 5d F-theorem
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• Disordered vector models: from higher spins to incipient strings
• Conformal bounds in three dimensions from entanglement entropy
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• On Large N Expansion of the Sphere Free Energy
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Interpolating between $a$ and $F$
• 3D ${\tau }_{RR}$-minimization in AdS${}_4$ gauged supergravity
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• Supersymmetric Graphene on Squashed Hemisphere