Ab initio holography

Lunts, Peter; Bhattacharjee, Subhro; Miller, Jonah; Schnetter, Erik; Kim, Yong Baek; Lee, Sung-Sik

doi:10.1007/jhep08(2015)107

Cited by 26 publications

(47 citation statements)

References 47 publications

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“…For gauge theories, it is the space of loops [9]. For vector models, it is the space of bi-local coordinates [13]. The operators satisfy the commutation relation [j n , j † m ] = δ n m .…”

Section: Jhep09(2016)044mentioning

confidence: 99%

“…(4.6) has no pre-imposed kinematic locality in the bulk because one has to include tensors associated with multi-local single-trace operators of all sizes. This kinematic non-locality is crucial in order to have a sense of diffeomorphism invariance in the bulk [13,31]. In the absence of kinematic locality in the bulk, the degree of locality in the classical geometry that emerges in the large N limit is determined dynamically.…”

Section: Jhep09(2016)044mentioning

confidence: 99%

“…(5.21) with δ = 0. In [13], based on numerical solutions in finite system sizes, it was argued that the hopping field exhibits a divergent length scale at finite z in the superfluid phase. However, this claim is incorrect: the apparent divergence 'observed' in the numerical solution is a finite size effect.…”

Section: Jhep09(2016)044mentioning

confidence: 99%

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Horizon as critical phenomenon

Lee

2016

J. High Energ. Phys.

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We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U(N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.

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Section: Jhep09(2016)044mentioning

confidence: 99%

Section: Jhep09(2016)044mentioning

confidence: 99%

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Horizon as critical phenomenon

Lee

2016

J. High Energ. Phys.

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“…In recent years, there have been various attempts to sharpen the idea so that we may derive the AdS/CFT from the first principle of the local (or quantum) renormalization group in the dual field theories [1][2][3][4][5][6] It is, however, still mysterious what kind of cut-off and renormalization prescription should be used or how the bulk locality emerges in the strongly coupled regime. See also [7] for a generalized viewpoint on the cut-off and the renormalization inspired by the bulk diffeomorphism.…”

Section: Jhep06(2015)092mentioning

confidence: 99%

“…We should also realize that the SL(2, Z) invariant "metric" ds 2 = 1 (Imτ ) 2 dτ dτ that appears in front of the (generalized) Riegert four derivative kinetic operator 6 (4) is related to the Zamolodchikov metric of the N = 4 super Yang-Mills theory. This is because the two-point functions of dimension four operators in d = 4 dimensions is logarithmically divergent in flat space-time as k 4 log k 2 and this is the origin of the four derivative terms with quadratic on τ in the conformal anomaly.…”

Section: Jhep06(2015)092mentioning

confidence: 99%

Local renormalization group functions from quantum renormalization group and holographic bulk locality

Nakayama

2015

J. High Energ. Phys.

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The bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the N = 4 super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographic renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar N = 4 super Yang-Mills theory.

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Exotic RG flows from holography

2017

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Holographic RG flows are studied in an Einstein‐dilaton theory with a general potential. The superpotential formalism is utilized in order to characterize and classify all solutions that are associated with asymptotically AdS space‐times. Such solutions correspond to holographic RG flows and are characterized by their holographic β‐functions. Novel solutions are found that have exotic properties from a RG point‐of view. Some have β‐functions that are defined patch‐wise and lead to flows where the β‐function changes sign without the flow stopping. Others describe flows that end in non‐neighboring extrema in field space. Finally others describe regular flows between two minima of the potential and correspond holographically to flows driven by the VEV of an irrelevant operator in the UV CFT.

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Ab initio holography

Cited by 26 publications

References 47 publications

Horizon as critical phenomenon

Horizon as critical phenomenon

Local renormalization group functions from quantum renormalization group and holographic bulk locality

Exotic RG flows from holography

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