Black Holes with Scalar Hair and Asymptotics in<i>N</i>= 8 Supergravity

Hertog, Thomas; Maeda, Kenichi

doi:10.1088/1126-6708/2004/07/051

Cited by 179 publications

(371 citation statements)

References 46 publications

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“…This points to the fact that, in the instanton vacuum, the CFT couples to a source. This situation is then somewhat reminiscent to the discussion in [28] where similar effects were found. Notice that in the trivial vacuum φ = 0 discussed in section 3, this effect is absent and at the linearized level the back-reaction can be neglected altogether, its effects appearing only at second order.…”

Section: Discussion and Outlooksupporting

confidence: 57%

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Instantons and conformal holography

Haro

Petkou

2006

J. High Energy Phys.

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We study a subsector of the AdS 4 /CFT 3 correspondence where a class of solutions in the bulk and on the boundary can be explicitly compared. The bulk gravitational theory contains a conformally coupled scalar field with a φ 4 potential, and is holographically related to a massless scalar with a φ 6 interaction in three dimensions. We consider the scalar sector of the bulk theory and match bulk and boundary classical solutions of the equations of motion. Of particular interest is the matching of the bulk and the boundary instanton solutions which underlies the relationship between bulk and boundary vacua with broken conformal invariance. Using a form of radial quantization we show that quantum states in the bulk correspond to multiply-occupied single particle quantum states in the boundary theory. This allows us to explicitly identify the boundary composite operator which is dual to the bulk scalar, at the free theory level as well as in the instanton vacuum. We conclude with a discussion of possible implications of our results.

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Section: Discussion and Outlooksupporting

confidence: 57%

“…In Classical Holography we should solve (28) imposing Dirichlet boundary conditions at r = 0 and regularity at r = ∞ as…”

Section: Instantons and The Vacuum Structure Of The Boundary Cftsmentioning

confidence: 99%

Instantons and conformal holography

Haro

Petkou

2006

J. High Energy Phys.

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“…Hairy black holes have been found in designer gravity [24 -26], for AdS-invariant boundary conditions (25) as well as for other choices of W . In all known examples, however, the boundary conditions render the usual AdS vacuum unstable.…”

Section: Designer Gravitymentioning

confidence: 99%

“…The connection between the validity of the no-hair conjecture and the absence of spherical static scalar solitons also means that the PET does exclude spherical scalar hair for all AdS-invariant designer gravity boundary conditions (25). This is because if there exists a soliton s r , then the conformally rescaled configurations r s r provide, for < 1= d ÿ 1 p , explicit examples of regular initial data with (arbitrary) negative mass [32,40].…”

Section: Designer Gravitymentioning

confidence: 99%

“…It is widely believed that spherical asymptotically flat black holes with scalar hair generally exist when the scalar potential has negative regions. 3 This is due, in part, to the proliferation in recent years of neutral [24,25] (and charged [26]) asymptotically AdS black hole solutions with scalar hair, where the scalar asymptotically tends to a local negative extremum of the potential. When this is a maximum (which we assume satisfies the BreitenlohnerFreedman (BF) bound [27]) the scalar generically decays slower than usual.…”

Section: Introductionmentioning

confidence: 99%

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Towards a novel no-hair theorem for black holes

Hertog

2006

Phys. Rev. D

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We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalarhair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

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A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

Naghdi

2018

Fortschritte der Physik

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From a consistent Kaluza-Klein truncation of 11-dimensional supergravity over AdS 4 × C P 3 S 1 /Z k , with a general 4-form ansatz, we arrive at a set of equations and solutions for the included fields. In particular, we have a bulk equation for a self-interacting (pseudo)scalar with arbitrary mass. By computing the energy-momentum tensors of the associated Einstein equations, to include the backreaction, and setting them to zero, we solve the resulting equations with the bulk one and get solutions corresponding to marginal and marginally relevant deformations of the boundary CFT 3 , which break the conformal symmetry. These bulk (pseudo)scalars are SU (4) × U (1)-singlet and the corresponding solutions break all supersymmetries and parity because of the associated (anti)M-branes wrapping around specific and mixed internal and external directions. As a result and according to AdS 4 /CFT 3 duality rules, we would realize the boundary counterpart in three-dimensional Chern-Simon U (N) field theories with matters in fundamental representations. In particular, we build a S O(4)-invariant Fubini-like instanton solution by setting a specific boundary Lagrangian. The resulting solution is used to describe the dynamics of thin-wall bubbles that cause instability and big crunch singularities in the bulk because of the unboundedness of the boundary double-hump potential from below. Relations to mass-deformed ABJM model, O(N) vector models and scale invariance breaking are also discussed. Meanwhile, we evaluate corrections for the background actions because of the bulk and boundary instantons.

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Black Holes with Scalar Hair and Asymptotics inN= 8 Supergravity

Cited by 179 publications

References 46 publications

Instantons and conformal holography

Instantons and conformal holography

Towards a novel no-hair theorem for black holes

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

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Black Holes with Scalar Hair and Asymptotics inN= 8 Supergravity

Cited by 179 publications

References 46 publications

Instantons and conformal holography

Instantons and conformal holography

Towards a novel no-hair theorem for black holes

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS4/CFT3

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Product

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About

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃