Propagators and effective potentials in anti-de Sitter space

We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to renormalized position space correlators. Several applications are presented, including the holographic boundary CFTs as well as spacelike boundary CFTs, which provide realizations of the pseudo-conformal universe.

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“…Notice that for ρ * → 0 we obtain 48) while for ρ * → ∞ we have b p → 0 and we recover the formula for a pure CFT.…”

Section: Two-point Function In Ads Slicingsupporting

confidence: 79%

Holographic CFTs on maximally symmetric spaces: Correlators, integral transforms, and applications

2015

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“…Integrating this relation over m 2 then determines the effective Lagrangian density [8,9,19,21]. Exactly equivalent results are obtained from mode expansions or using zeta functions [9,14,20,22].…”

Section: Scalar Effective Action In Gravitational Backgroundsmentioning

confidence: 99%

“…Exactly equivalent results are obtained from mode expansions or using zeta functions [9,14,20,22]. The Feynman propagators for massive scalars in AdS d [14,19] and dS d [8] have the forms: Lagrangian density [8,9,19,21], and in higher dimensions this procedure can be taken as a definition of the corresponding effective Lagrangian density. It is clear already from (3.2) and (3.3) that odd and even dimensions are very different.…”

Section: Scalar Effective Action In Gravitational Backgroundsmentioning

confidence: 99%

Large-order perturbation theory and de Sitter/anti–de Sitter effective actions

Das

Dunne

2006

Phys. Rev. D

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We analyze the large-order behavior of the perturbative weak-field expansion of the effective Lagrangian density of a massive scalar in de Sitter and anti de Sitter space, and show that this perturbative information is not sufficient to describe the non-perturbative behavior of these theories, in contrast to the analogous situation for the Euler-Heisenberg effective Lagrangian density for charged scalars in constant electric and magnetic background fields. For example, in even dimensional de Sitter space there is particle production, but the effective Lagrangian density is nevertheless real, even though its weak-field expansion is a divergent non-alternating series whose formal imaginary part corresponds to the correct particle production rate. This apparent puzzle is resolved by considering the full non-perturbative structure of the relevant Feynman propagators, and cannot be resolved solely from the perturbative expansion. * Electronic address: das@pas.rochester.edu † Electronic address: dunne@phys.uconn.edu

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“…This is indeed the case, as we now check. The bulk AdS Poincaré propagator has the form [74,75], (8.19) where…”

Section: Jhep09(2014)073mentioning

confidence: 99%

Holography of the BTZ black hole, inside and out

Fuente

Sundrum

2014

J. High Energ. Phys.

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We propose a 1 + 1 dimensional CFT dual structure for quantum gravity and matter on the extended 2 + 1 dimensional BTZ black hole, realized as a quotient of the Poincaré patch of AdS 3 . The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincaré patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.

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Propagators and effective potentials in anti-de Sitter space

Cited by 197 publications

References 6 publications

Holographic CFTs on maximally symmetric spaces: Correlators, integral transforms, and applications

Holographic CFTs on maximally symmetric spaces: Correlators, integral transforms, and applications

Large-order perturbation theory and de Sitter/anti–de Sitter effective actions

Holography of the BTZ black hole, inside and out

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