Locality and anomalies in warped conformal field theory

Jensen, Kristan

doi:10.1007/jhep12(2017)111

Cited by 39 publications

(65 citation statements)

References 81 publications

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“…Examples of theories with z ¼ ∞ anisotropic scaling symmetry based on warped conformal field theories are discussed in Refs. [15,16].…”

Section: Discussionmentioning

confidence: 99%

“…One can show this, without loss of generality, 11 There are indeed examples of z ≠ 2 theories without particle number symmetry; see, for example, Refs. [15,16,32].…”

Section: Appendix: Diagonalizable and Finite Dimensional Dilatation Gmentioning

confidence: 99%

“…By contrast, in the models presented in Refs. [15,16], where N ¼ 0 and the Lagrangian is invariant under x → x and t → λt, arbitrary powers of spatial derivatives are allowed.…”

Section: Explicit (D + 1)-dimensional Examplesmentioning

confidence: 99%

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Existence and construction of Galilean invariant z≠2 theories

Grinstein

Pal

2018

Phys. Rev. D

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We prove a no-go theorem for the construction of a Galilean boost invariant and z ≠ 2 anisotropic scale invariant field theory with a finite dimensional basis of fields. Two point correlators in such theories, we show, grow unboundedly with spatial separation. Correlators of theories with an infinite dimensional basis of fields, for example, labeled by a continuous parameter, do not necessarily exhibit this bad behavior. Hence, such theories behave effectively as if in one extra dimension. Embedding the symmetry algebra into the conformal algebra of one higher dimension also reveals the existence of an internal continuous parameter. Consideration of isometries shows that the nonrelativistic holographic picture assumes a canonical form, where the bulk gravitational theory lives in a space-time with one extra dimension. This can be contrasted with the original proposal by Balasubramanian and McGreevy, and by Son, where the metric of a (d þ 2)-dimensional space-time is proposed to be dual of a d-dimensional field theory. We provide explicit examples of theories living at fixed point with anisotropic scaling exponent z ¼ 2l lþ1 , l ∈ Z.

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“…Examples of theories with z ¼ ∞ anisotropic scaling symmetry based on warped conformal field theories are discussed in Refs. [15,16].…”

Section: Discussionmentioning

confidence: 99%

“…One can show this, without loss of generality, 11 There are indeed examples of z ≠ 2 theories without particle number symmetry; see, for example, Refs. [15,16,32].…”

Section: Appendix: Diagonalizable and Finite Dimensional Dilatation Gmentioning

confidence: 99%

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Existence and construction of Galilean invariant z≠2 theories

Grinstein

Pal

2018

Phys. Rev. D

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“…One of the best non-CFT theories one could consider to study such questions and developing various tools that have already been established for CFTs, is actually the warped conformal field theories (WCFTs) and its duality with warped AdS space times, (WAdS 3 /WCFT 2 ) [15][16][17][18][19][20][21][22][23]. One reason this duality is very useful is that warped CFTs contain enough symmetries that many techniques of normal CFTs could still be applied.…”

Section: Introductionmentioning

confidence: 99%

“…We show how two different cutoffs are needed, one for each field, and then how this affects the form of the entangler function and consequently the path-integral complexity. Then, in sections 3.3, we consider a scalar and a Weylfermion model of WCFTs where their specific actions have been derived in [20,22]. For these models, we explain how each parameter of the theory plays a role in the optimization procedure and therefore the path-integral computation complexity.…”

Section: Introductionmentioning

confidence: 99%

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

Ghodrati

2020

J. High Energ. Phys.

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Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals

Wen

2019

J. High Energ. Phys.

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Based on the Lewkowycz-Maldacena prescription and the fine structure analysis of holographic entanglement proposed in [1], we explicitly calculate the holographic entanglement entropy for warped CFT that duals to AdS 3 with a Dirichlet-Neumann type of boundary conditions. We find that certain type of null geodesics emanating from the entangling surface ∂A relate the field theory UV cutoff and the gravity IR cutoff. Inspired by the construction, we furthermore propose an intrinsic prescription to calculate the generalized gravitational entropy for general spacetimes with non-Lorentz invariant duals. Compared with the RT formula, there are two main differences. Firstly, instead of requiring that the bulk extremal surface E should be anchored on ∂A, we require the consistency between the boundary and bulk causal structures to determine the corresponding E. Secondly we use the null geodesics (or hypersurfaces) emanating from ∂A and normal to E to regulate E in the bulk. We apply this prescription to flat space in three dimensions and get the entanglement entropies straightforwardly. arXiv:1810.11756v3 [hep-th] 29 Jan 20191 The extremal condition is the result of imposing the equations of motion and replica symmetry on all the fields in the action. In [13], as the gauge fields are nondynamical and do not appear in the symplectic structure, thus should not be imposed with the replica symmetry (or periodic) condition. As a result, in that case the geometric quantity E that measures the entanglement entropy is not an extremal surface. See [14] for a simpler discussion on the extremal condition.2 A proof for the homology constraint at topological level in AdS/CFT is given in [19] 3 Although the AdS/CFT has attracted most of the attentions, the holographic principle is assumed to be hold for general spacetimes. So far the holography beyond AdS/CFT that has been proposed include the dS/CFT correspondence [20], the Lifshitz spacetime/Lifshitz-type field theory duality [21][22][23][24], the Kerr/CFT correspondence [25], the WAdS/CFT [26,27] or WAdS/WCFT [28,29] correspondence, and flat holography in four dimensions [30][31][32] and three dimensions [33][34][35].

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Locality and anomalies in warped conformal field theory

Cited by 39 publications

References 81 publications

Existence and construction of Galilean invariant z≠2 theories

Existence and construction of Galilean invariant z≠2 theories

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals

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