PIRSA:12100054

Constraining RG flow in three-dimensional field theory

Safdi, B. (2012). Constraining RG flow in three-dimensional field theory. Perimeter Institute. https://pirsa.org/12100054

Safdi, Benjamin. Constraining RG flow in three-dimensional field theory. Perimeter Institute, Oct. 16, 2012, https://pirsa.org/12100054 

          @misc{ pirsa_PIRSA:12100054,
            doi = {10.48660/12100054},
            url = {https://pirsa.org/12100054},
            author = {Safdi, Benjamin},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Constraining RG flow in three-dimensional field theory},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {oct},
            note = {PIRSA:12100054 see, \url{https://pirsa.org}}
          }

Benjamin Safdi Massachusetts Institute of Technology (MIT)

Talk numberPIRSA:12100054
DOI10.48660/12100054
Collection
Talk Type Scientific Series
Subject

Abstract

The entanglement entropy S(R) across a circle of radius R has been invoked recently in deriving general constraints on renormalization group flow in three-dimensional field theory.  At conformal fixed points, the negative of the finite part of the entanglement entropy, which is called F, is equal to the free energy on the round three-sphere. The F-theorem states that F decreases under RG flow. Along the RG flow it has recently been shown that the renormalized entanglement entropy {\cal F}(R) = -S(R) + R S'(R), which is equal to F at the fixed points, is a monotonically decreasing function.  I will review various three-dimensional field theories where we can calculate F on the three-sphere and compute its change under RG flow, including free field theories, perturbative fixed points, large N field theories with double trace deformations, gauge theories with large numbers of flavors, and supersymmetric theories with at least {\cal N} = 2 supersymmetry.  I will also present calculations of the renormalized entanglement entropy along the RG flow in free massive field theory and in holographic examples.