Instantons and conformal holography

Physical Review D, 1999

Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity ͑at least with a negative cosmological constant͒ can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay, and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taubbolt spacetimes, and compare them to a ͑2ϩ1͒-dimensional conformal field theory ͑at large N͒ compactified on a squashed three-sphere and on the twisted plane. ͓S0556-2821͑99͒06302-X͔

Physical Review Letters, 2007

We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M-theory. The holographic effective potential is exactly calculated, allowing us to study non-perturbatively the stability of AdS4 in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS4 space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.

Physics Letters B, 1998

Classical and Quantum Gravity

2010

We present a self-gravitating dyon solution of the Einstein-Yang-Mills-Higgs equations of motion in asymptotically AdS space. The back reaction of gauge and Higgs fields on the space-time geometry leads to the metric of an asymptotically AdS black hole. Using the gauge/gravity correspondence we analyze relevant properties of the finite temperature quantum field theory defined on the boundary. In particular we identify an order operator, characterize a phase transition of the dual theory on the border and also compute the expectation value of the finite temperature Wilson loop. * Associated with CICBA

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.

PHYSICAL REVIEW D 104, 064026 (2021), 2021

We study non-Einstein Bach-flat gravitational instanton solutions that can be regarded as the generalization of the Taub-NUT/bolt and Eguchi-Hanson solutions of Einstein gravity to conformal gravity. These solutions include non-Einstein spaces which are either asymptotically locally flat spacetimes or asymptotically locally anti-de Sitter (AlAdS). Nevertheless, solutions with different asymptotic conditions exist: we find geometries that present a weakened AlAdS asymptotia, exhibiting the typical low decaying mode of conformal gravity. This permits us to identify the simple Neumann boundary condition that, as it happens in the asymptotically AdS sector, selects the Einstein solution out of the solutions of conformal gravity. All the geometries present nonvanishing Hirzebruch signature and Euler characteristic, being single-centered instantons. We compute the topological charges as well as the Noether charges of the Taub-NUT/bolt and Eguchi-Hanson spacetimes, which happen to be finite. This enables us to study the thermodynamic properties of these geometries.

Physics Letters B, 2002

An explicit holographic correspondence between AdS bulk and boundary quantum states is found in the form of a one to one mapping between scalar field creation/annihilation operators. The mapping requires the introduction of arbitrary energy scales and exhibits an ultraviolet-infrared duality: a small regulating mass in the boundary theory corresponds to a large momentum cutoff in the bulk. In the massless (conformal) limit of the boundary theory the mapping covers the whole field spectrum of both theories. The mapping strongly depends on the discretization of the field spectrum of compactified AdS space in Poincare coordinates. *

Journal of High Energy Physics, 2016

Assuming the existence of a field theory in D dimensions dual to (D + 1)dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk-2d boundary case and then focus on the 4d bulk-3d boundary example, where the symmetry in question is the infinite dimensional BMS 4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D = 4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.

Journal of High Energy Physics, 2008

We continue the studies of our earlier proposal for an AdS/CFT correspondence for timedependent supergravity backgrounds. We note that by performing a suitable change of variables, the dual super Yang-Mills theory lives on a flat base space, and the time-dependence of the supergravity background is entirely encoded in the time-dependent couplings (gauge and axionic) and their supersymmetric completion. This form of the SYM allows a detailed perturbative analysis to be performed. In particular the one-loop Wilsonian effective action of the boundary SYM theory is computed. By using the holographic UV/IR relation, we propose a way to extract the bulk metric from the Wilsonian effective action; and we find that the bulk metric of our supergravity solutions can be reproduced precisely. While the bulk geometry can have various singularities such as geodesic incompleteness, gauge theory quantum effects can introduce higher derivative corrections in the effective action which can serve as a way to resolve the singularities.