AUTHOR=Taylor Marika , Woodhead William TITLE=The Holographic F Theorem JOURNAL=Frontiers in Physics VOLUME=5 YEAR=2017 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00066 DOI=10.3389/fphy.2017.00066 ISSN=2296-424X ABSTRACT=

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension 3/2 < Δ < 5/2. Therefore, the strongest version of the F theorem is in general violated.