Holographic renormalisation group flows and renormalisation from a Wilsonian perspective
Holographic renormalisation group flows and renormalisation from a Wilsonian perspective
From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, which have a diagonal evolution close to the fixed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss different renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group flows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space.
1-62
Lizana, J.M.
43ad7027-9522-456e-be2f-991f09a57396
Morris, T.R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Pérez-Victoria, M.
92b4e802-3fca-4c3a-8645-c2d83266b2c1
Lizana, J.M.
43ad7027-9522-456e-be2f-991f09a57396
Morris, T.R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Pérez-Victoria, M.
92b4e802-3fca-4c3a-8645-c2d83266b2c1
Lizana, J.M., Morris, T.R. and Pérez-Victoria, M.
(2016)
Holographic renormalisation group flows and renormalisation from a Wilsonian perspective.
Journal of High Energy Physics, 2016 (198), .
(doi:10.1007/JHEP03(2016)198).
Abstract
From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, which have a diagonal evolution close to the fixed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss different renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group flows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space.
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Accepted/In Press date: 2 March 2016
e-pub ahead of print date: 30 March 2016
Organisations:
Theoretical Partical Physics Group
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Local EPrints ID: 397590
URI: http://eprints.soton.ac.uk/id/eprint/397590
PURE UUID: ff39cc35-3cc2-432c-b73e-b669807719a8
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Date deposited: 04 Jul 2016 12:20
Last modified: 15 Mar 2024 02:36
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Author:
J.M. Lizana
Author:
M. Pérez-Victoria
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