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- Constraining RG flow in three-dimensional field theory

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12100054

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.

©2012 Institut Périmètre de Physique Théorique