Holographic QFTs on S2×S2, spontaneous symmetry breaking and Efimov saddle points

Kiritsis, Elias; Nitti, Francesco; Preau, Edwan

doi:10.1007/jhep08(2020)138

“…There may be a distributional limit for the source term which exactly matches the behavior of the CdL solution as Λ → ∞, but this is not evident 53. Similar solutions where discussed for general S d 1 × S d 2 foliations in pure gravity[51], and recently for S 2 × S 2 foliations in Einstein-dilaton theory[52].…”

mentioning

confidence: 81%

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

Ghosh,

Kiritsis,

Nitti

et al. 2021

Preprint

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Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension ∆ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on R × S 3 .

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“…We can instead define the boundary conditions on the gravity side in order to accommodate the CdL geometry as an allowed solution. Provided one can do this consistently, 52 this defines a different field theory on the cylinder, which does not admit the global AdS solution as one its states. This theory can only be extended up to a finite global time, at which point the time-evolution reaches a singularity as a consequence of an infinite instantaneous "kick" at ψ = π/2.…”

Section: Jhep09(2021)065mentioning

confidence: 99%

“…The relevant expansions are given in [13,16] and we refer the reader to these works for details. Without loss of generality we consider a UV fixed point at an extremum of V at ϕ = 0 with the potential in the vicinity 53 Similar solutions where discussed for general S d 1 × S d 2 foliations in pure gravity [51], and recently for S 2 × S 2 foliations in Einstein-dilaton theory [52].…”

Section: Jhep09(2021)065mentioning

confidence: 99%

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

Ghosh

¹

,

Kiritsis²,

Nitti³

et al. 2021

J. High Energ. Phys.

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Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension ∆ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on R × S3.

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“…A similar case with the S 2 factor replaced by S 3 was studied in [11]. Euclidean solutions with boundary S m × S n (without a time direction) were studied in [3] (see also [12] for when m = 2 and [13] for when m = n = 2). Finally, when the boundary is R × S 2 × S 2 , which is the case we study in appendix D, black hole solutions were discussed in [11], but the dependence of the solutions on the ratio of the spheres at the conformal boundary was not analyzed.…”

Section: Introductionmentioning

confidence: 99%

An infinity of black holes

Ye¹,

Wang²,

Horowitz³

2022

Class. Quantum Grav.

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In general relativity (without matter), there is typically a one parameter family of static, maximally symmetric black hole solutions labelled by their mass. We show that there are situations with many more black holes. We study asymptotically anti-de Sitter solutions in six and seven dimensions having a conformal boundary which is a product of spheres cross time. We show that the number of families of static, maximally symmetric black holes depends on the ratio, λ, of the radii of the boundary spheres. As λ approaches a critical value, λc, the number of such families becomes inﬁnite. In each family, we can take the size of the black hole to zero, obtaining an inﬁnite number of static, maximally symmetric non-black hole solutions. We discuss several applications of these results, including Hawking-Page phase transitions and the phase diagram of dual ﬁeld theories on a product of spheres, new positive energy conjectures, and more.

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Holographic QFTs on S2×S2, spontaneous symmetry breaking and Efimov saddle points

Cited by 5 publications

References 42 publications

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

An infinity of black holes

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