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AdS/CFT Duality and Holographic Renormalization Group: A Review

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arxiv 2412.05446 v1 pith:4MIQL2YH submitted 2024-12-06 hep-th cond-mat.stat-mech

Han Huang This is my paper · ORCID
classification hep-thcond-mat.stat-mech
keywords dualityholographicrenormalizationthentheoryflowsgroupreview
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In this paper we review aspects of anti de Sitter/conformal field theory (AdS/CFT) duality and the notion of holographic renormalization group (RG) flow. We start by discussing supersymmetry and construct the N = 4 super Yang-Mills theory in d = 4 by Kaluza-Klein dimensional reduction method. Then, we study the large-N limit and how it leads to the AdS/CFT duality. Using AdS/CFT, we then study the super-gravitational dual flows to the RG flows in CFT generated by marginal and relevant deformations, using the N = 4 super Yang-Mills theory as an example. Then, we prove the Zamolodchikov C-theorem holographically. Finally, we discuss the Wilsonian holographic renormalization.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strongly Coupled Continuous Time Crystal

    quant-ph 2025-07 reject novelty 4.0 of 10

    The authors claim that continuous time crystals in strongly correlated lattice bosons are holographically dual to charged AdS black holes, yielding a critical temperature formula and a universal scaling law.

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    comes from the transformation a → et/2a. Using Φ i = ∂ ∂g i L(g, a, x) and ∂¯zT + ∂zΘ = 0, we find that 1 2 βi∂iF (g, x) = 3βiHi − βiβk∂kHi − βk ∂kβi Hi (38) and βk∂kHi + ∂iβk Hk − Hi = −2βkGik + βjβkGij + βj ∂iβk Gjk + βj ∂jβk Gik (39) Define C(g) = F (g) + 4βiHi = 6βiβjGij (...

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