Holographic description of quantum field theory

Nuclear Physics B (Impact Factor: 3.93). 12/2009; 832(3). DOI: 10.1016/j.nuclphysb.2010.02.022
Source: arXiv


We propose that general D-dimensional quantum field theories are dual to (D+1)-dimensional local quantum theories which in general include objects with spin two or higher. Using a general prescription, we construct a (D+1)-dimensional theory which is holographically dual to the D-dimensional O(N) vector model. From the holographic theory, the phase transition and critical properties of the model in dimensions D>2 are described. Comment: 23 pages, 1 figure; v2) references added; appendix expanded

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    • "Additional contributions were made for example by [5] [6] [7] [8] [9] [10] and more recent discussions include [11] [12] [13] (see also [14]). However, a comprehensive understanding from the " boundary to bulk " perspective of the relationship between RG and holography still remains elusive, because of the lack of technology to control the RG flow of a generic, strongly coupled conformal field theory (see [15] [16] for some progress in this direction. 1 ) "
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    ABSTRACT: We continue to study the holographic dual of free $U(N)$ vector models in the single-trace sector on $\mathbb{R}^{1,d-1}$ (for $d$ odd) from a renormalization group point of view, following the previous papers arXiv:1402.1430v2 and arXiv:1407.4574v2. The bulk dual derived from ERG has been shown to reproduce all of the correlation functions of the free fixed point. This bulk higher spin theory contains interactions amongst all of the higher spin fields that are apparently non-local. In this paper, we show that truncating the bulk theory to linearized level reproduces the Fronsdal equations on $AdS_{d+1}$ for all higher spin fields, with the correct boundary conditions. More precisely, we establish canonical equivalence between linearized renormalization group equations of free $U(N)$ vector models in the single-trace sector, and $AdS_{d+1}$ Fronsdal equations.
    Full-text · Article · Mar 2015 · Journal of High Energy Physics
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    • "The procedure is based on integrating out shells of geometry along the radial direction, while keeping the overall path integral fixed. Other recent developments on the subject include [20] [21] [22] [23] [24] [25] [26] [27] [28]. "
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    ABSTRACT: We propose a method for determining the exact correspondence between the Wilsonian cut-off scale on the boundary and its holographically dual bulk theory. We systematically construct the multi-trace Wilsonian effective action from holographic renormalisation and evolve it by integrating out the asymptotically Anti-de Sitter bulk geometry with scalar probes. The Wilsonian nature of the effective action is shown by proving that it must be either double-trace, closing in on itself under successive integrations, or have an infinite series of multi-trace terms. Focusing on composite scalar operator renormalisation, we relate the Callan-Symanzik equation, the flow of the scalar anomalous dimension and the multi-trace beta functions to their dual RG flows in the bulk. Establishing physical renormalisation conditions on the behaviour of the large-$N$ anomalous dimension then enables us to extract the energy scales. Examples of pure AdS, GPPZ flow, black brane in AdS, M2 and M5 branes are studied before we generalise our results to arbitrary numbers of mass and thermal deformations of an ultra-violet CFT. Relations between the undeformed Wilsonian cut-off, deformation scales and the deformed Wilsonian cut-off are discussed, as is phenomenology of each considered background. We see how a mass gap, the emergent infra-red CFT scaling, etc. arise in different effective theories. We also argue that these results can have alternative interpretations through the flow of the conformal anomaly or the Ricci scalar curvature of boundary branes. They show consistency with the c-theorem.
    Full-text · Article · Dec 2011 · Journal of High Energy Physics
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    • "Recently a number of authors have proposed using renormalization ideas in the spirit of Wilson in holographic descriptions of strongly coupled gauge theories [1] [2] [3] [4] [5] [6] [7] [8]. (For earlier discussions, see [9] [10] [11] [12] [13] [14]) The radial direction in AdS like spaces is dual to energy scale in the field theory [15] [16] [17] [18] and one can imagine introducing a cut-off at some finite radius, splitting the supergravity solution in two. "
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    ABSTRACT: We explore the role of a holographic Wilsonian cut-off in simple probe brane models with chiral symmetry breaking/restoration phase transitions. The Wilsonian cut-off allows us to define supergravity solutions for off-shell configurations and hence to define a potential for the chiral condensate. We pay particular attention to the need for configurations whose action we are comparing to have the same IR and UV boundary conditions. We exhibit new first and second order phase transitions with changing cut-off. We derive the effective potential for the condensate including mean field and BKT type continuous transitions.
    Preview · Article · Jul 2011 · Physical review D: Particles and fields
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