Loops in AdS: from the spectral representation to position space. Part II

Carmi, Dean

doi:10.1007/jhep07(2021)186

Cited by 22 publications

(21 citation statements)

References 73 publications

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“…However, in AdS, it is often much easier to analytically solve the bootstrap equations than it is to evaluate Witten diagrams. This idea has led to the evaluation of a large amount of CFT data in theories with weakly coupled bulk duals [37,[39][40][41][42][121][122][123][124][125][126][127][128].…”

Section: Constraints On Gravitational Theories In Adsmentioning

confidence: 99%

Snowmass White Paper: The Analytic Conformal Bootstrap

Hartman¹,

Mazáč²,

Simmons-Duffin³

et al. 2022

Preprint

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The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered by the development of new Lorentzian methods, it has been used to solve conformal field theories at large spin; to place bounds on energy distributions, event shapes, operator product coefficients, and other observables; and to understand aspects of quantum gravity in anti-de Sitter space. We review these advances and highlight several promising areas for future exploration. Targets include developing new methods to close the gap between numerical and analytic bounds, extending the bootstrap beyond conformal fixed points, applications to quantum gravity and cosmology, and building on ties to condensed matter theory and mathematics.

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Section: Constraints On Gravitational Theories In Adsmentioning

confidence: 99%

Snowmass White Paper: The Analytic Conformal Bootstrap

Hartman¹,

Mazáč²,

Simmons-Duffin³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Candy Witten diagrams in EAdS have been considered in various works e.g. [125,[133][134][135][136][137][138][139][140][141] using a variety of techniques. It can also be computed in the Mellin-Barnes representation, for instance using the cutting rules and dispersion formula given in section 2.3.…”

Section: Jhep12(2021)074mentioning

confidence: 99%

From dS to AdS and back

Sleight

Taronna

2021

J. High Energ. Phys.

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We describe in more detail the general relation uncovered in our previous work between boundary correlators in de Sitter (dS) and in Euclidean anti-de Sitter (EAdS) space, at any order in perturbation theory. Assuming the Bunch-Davies vacuum at early times, any given diagram contributing to a boundary correlator in dS can be expressed as a linear combination of Witten diagrams for the corresponding process in EAdS, where the relative coefficients are fixed by consistent on-shell factorisation in dS. These coefficients are given by certain sinusoidal factors which account for the change in coefficient of the contact sub-diagrams from EAdS to dS, which we argue encode (perturbative) unitary time evolution in dS. dS boundary correlators with Bunch-Davies initial conditions thus perturbatively have the same singularity structure as their Euclidean AdS counterparts and the identities between them allow to directly import the wealth of techniques, results and understanding from AdS to dS. This includes the Conformal Partial Wave expansion and, by going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the Froissart-Gribov inversion formula. We give a few (among the many possible) applications both at tree and loop level. Such identities between boundary correlators in dS and EAdS are made manifest by the Mellin-Barnes representation of boundary correlators, which we point out is a useful tool in its own right as the analogue of the Fourier transform for the dilatation group. The Mellin-Barnes representation in particular makes manifest factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS, which imply Cutkosky cutting rules and dispersion formulas for boundary correlators in (EA)dS. Our results are completely general and in particular apply to any interaction of (integer) spinning fields.

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“…They will be multiplied by the appropriate tensor structure. Thus, the fermionic contact Witten diagram can be written in terms of scalar contact Witten diagram W fermion ∝ D 1111 [47,48]. We compute the correlation functions using appropriate Witten diagram to arrive at the following correlation functions It is possible to compute the first order correction also for massive fermions, using the identity…”

Section: Jhep12(2021)094mentioning

confidence: 99%

“…We have used the chiral projector P ± = (1 ± γ 0 )/2, while Π denotes the corresponding propagator of the scalar operator in AdS. For the purposes of perturbation theory, we note the following identity for the product of propagators [45][46][47] Σ ∆ (y, x; x 1 ) Σ ∆ (y, x;…”

Section: Jhep12(2021)094mentioning

confidence: 99%

Towards bootstrapping RG flows: sine-Gordon in AdS

Antunes

Costa

Penedones

et al. 2021

J. High Energ. Phys.

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The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS2, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.

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Loops in AdS: from the spectral representation to position space. Part II

Cited by 22 publications

References 73 publications

Snowmass White Paper: The Analytic Conformal Bootstrap

Snowmass White Paper: The Analytic Conformal Bootstrap

From dS to AdS and back

Towards bootstrapping RG flows: sine-Gordon in AdS

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