Evaluation of conformal integrals

Bzowski, Adam; McFadden, Paul; Skenderis, Kostas

doi:10.1007/jhep02(2016)068

Cited by 66 publications

(115 citation statements)

References 74 publications

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“…Similarly, the d dimensional trace reduces to a tadpole integral upon using identity (27). This is in accord with the fact that the Dirac Lagrangian density is classically Weyl invariant in all dimensions with a d-dependent scaling of the fermions.…”

Section: Expectation Value Of the Stress Tensor At O(h)mentioning

confidence: 54%

“…Furthermore the terms involving η αβ or η ρσ , can be written as two-point function integrals, defined in equation (26), using identities analogous to (27). Terms with more than one η reduce to tadpole integrals, which vanish, or integrals of the form…”

Section: Expectation Value Of the Stress Tensor At O(hmentioning

confidence: 99%

“…where we have used an identity similar to identity (27) and reparametrised the variable of integration k in the first equality, and equation (C.5) and the definition of the two-point function integral, (26), in the second equality. Therefore, substituting into equation (98) and using the Weyl-invariance of the 2-point function in d-dimensions, (32),…”

Section: Ip·(x−y)−iq·(z−y) H ρσ (Y)mentioning

confidence: 99%

“…Of course, the coefficients of the spin-1 2 conformal anomaly have been known for a long time and have been determined by various different methods, via one-loop divergences and heat kernel expansions [4,5,[13][14][15]17], conformal higher spins [12], path integral methods [20,21], or by QFT in curved spacetime methods [22,23]. The trace anomaly appears in the TTT correlator in CFT; the general structure of this correlator has been studied in [24][25][26][27]-moreover, in [24] the 3-point function of stress tensors for free fields is calculated in x-space. Curiously, however, to the best of our knowledge, this computation has never been done à la CapperDuff up to O(h 2 ).…”

Section: Introductionmentioning

confidence: 99%

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A rederivation of the conformal anomaly for spin-${\frac{1}{2}}$

Godazgar

Nicolai

2018

Class. Quantum Grav.

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We rederive the conformal anomaly for spin-1 2 fermions by a genuine Feynman graph calculation, which has not been available so far. Although our calculation merely confirms a result that has been known for a long time, the derivation is new, and thus furnishes a method to investigate more complicated cases (in particular concerning the significance of the quantum trace of the stress tensor in non-conformal theories) where there remain several outstanding and unresolved issues.

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Section: Expectation Value Of the Stress Tensor At O(h)mentioning

confidence: 54%

Section: Expectation Value Of the Stress Tensor At O(hmentioning

confidence: 99%

Section: Ip·(x−y)−iq·(z−y) H ρσ (Y)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A rederivation of the conformal anomaly for spin-${\frac{1}{2}}$

Godazgar

Nicolai

2018

Class. Quantum Grav.

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“…Conformal structures in Fourier space have been widely studied in the literature, see e.g. [23,29,36,88,103,104,109,111,112,[146][147][148][149][150][151][152]. In the following we will emphasise some simple properties of the Mellin-Barnes representation, which appear to have been little explored (to the best of our knowledge).…”

Section: C2 Fourier Transform Of Three-point Conformal Structuresmentioning

confidence: 99%

Bootstrapping inflationary correlators in Mellin space

Sleight

Taronna

2020

J. High Energ. Phys.

198

293

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We develop a Mellin space approach to boundary correlation functions in anti-de Sitter (AdS) and de Sitter (dS) spaces. Using the Mellin-Barnes representation of correlators in Fourier space, we show that the analytic continuation between AdS d+1 and dS d+1 is encoded in a collection of simple relative phases. This allows us to determine the late-time tree-level three-point correlators of spinning fields in dS d+1 from known results for Witten diagrams in AdS d+1 by multiplication with a simple trigonometric factor. At four point level, we show that Conformal symmetry fixes exchange four-point functions both in AdS d+1 and dS d+1 in terms of the dual Conformal Partial Wave (which in Fourier space is a product of boundary three-point correlators) up to a factor which is determined by the boundary conditions. In this work we focus on late-time four-point correlators with external scalars and an exchanged field of integer spin-. The Mellin-Barnes representation makes manifest the analytic structure of boundary correlation functions, providing an analytic expression for the exchange four-point function which is valid for general d and generic scaling dimensions, in particular massive, light and (partially-)massless fields. It moreover naturally identifies boundary correlation functions for generic fields with multivariable Meijer-G functions. When d = 3 we reproduce existing explicit results available in the literature for external conformally coupled and massless scalars. From these results, assuming the weak breaking of the de Sitter isometries, we extract the corresponding correction to the inflationary three-point function of general external scalars induced by a general spin-field at leading order in slow roll. These results provide a step towards a more systematic understanding of de Sitter observables at tree level and beyond using Mellin space methods.

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A Mellin space approach to cosmological correlators

Sleight

2020

J. High Energ. Phys.

161

193

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We propose a Mellin space approach to the evaluation of late-time momentumspace correlation functions of quantum fields in (d + 1)-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general d framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including n-point contact diagrams and 4-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for d = 3 and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum space boundary correlators in (d + 1)-dimensional anti-de Sitter space (Witten diagrams).

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Evaluation of conformal integrals

Cited by 66 publications

References 74 publications

A rederivation of the conformal anomaly for spin-${\frac{1}{2}}$

A rederivation of the conformal anomaly for spin-${\frac{1}{2}}$

Bootstrapping inflationary correlators in Mellin space

A Mellin space approach to cosmological correlators

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