The holographic F theorem

Marika Taylor; William Woodhead

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arXiv · 1604.06809

The holographic F theorem

Marika Taylor·William Woodhead

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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 $3/2 < \Delta < 5/2$. Therefore the strongest version of the F theorem is in general violated.

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Marika Taylor, William Woodhead. 2016-04-22. The holographic F theorem. https://arxiv.org/abs/1604.06809

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