The holographic F theorem
The holographic F theorem
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.
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Woodhead, William
2af6629c-0b18-47cf-b751-975beb5e5652
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Woodhead, William
2af6629c-0b18-47cf-b751-975beb5e5652
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.
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fphy-05-00066
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Accepted/In Press date: 4 December 2017
e-pub ahead of print date: 18 December 2017
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Local EPrints ID: 416704
URI: http://eprints.soton.ac.uk/id/eprint/416704
ISSN: 0429-7725
PURE UUID: 2f2231f3-3137-4e55-ab51-53715736f3f9
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Date deposited: 05 Jan 2018 17:30
Last modified: 16 Mar 2024 04:10
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Author:
William Woodhead
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