Holographic Lifshitz flows

A bstract Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or ‘Lifshitz’) exponent z . Hence, a rich variety of possible RG flows arises. The first example is already given by the standard non-relativistic limit, which can be viewed as...

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Bibliographic Details
Published in:The journal of high energy physics 2024-09, Vol.2024 (9), p.175-34, Article 175
Main Authors: Baggioli, Matteo, Pujolàs, Oriol, Wu, Xin-Meng
Format: Article
Language:English
Subjects:
AdS-CFT Correspondence
Classical and Quantum Gravitation
Couplings
Elementary Particles
Fields (mathematics)
Gauge-Gravity Correspondence
Graphene
Gravity
Holography
Invariance
Phenomenology
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Renormalization Group
Space-Time Symmetries
String Theory
Symmetry
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Summary:A bstract Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or ‘Lifshitz’) exponent z . Hence, a rich variety of possible RG flows arises. The first example is already given by the standard non-relativistic limit, which can be viewed as the flow from a z = 1 UV fixed point to a z = 2 IR fixed point. In strongly coupled theories, there are good arguments suggesting that Lorentz invariance can emerge dynamically in the IR from a Lorentz violating UV. In this work, we perform a generic study of fixed points and the possible RG flows among them in a minimal bottom-up holographic model without Lorentz invariance, aiming to shed light on the possible options and the related phenomenology. We find: i) A minor generalization of previous models involving a massive vector field with allowed self-couplings leads to a much more efficient emergence of Lorentz invariance than in the previous attempts. Moreover, we find that generically the larger is the UV dynamical exponent z UV the faster is the recovery of Lorentz symmetry in the IR. ii) We construct explicitly a holographic model with a line of fixed points, realizing different Lifshitz scaling along the line. iii) We also confirm the monotonicity of a recently proposed a-function along all our Lorentz violating RG flows.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP09(2024)175