Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension

Isono, Hiroshi; Noumi, Toshifumi; Shiu, Gary

doi:10.1007/jhep10(2019)183

Cited by 58 publications

(59 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Even though there exist technical complications associated to spins and helicities, it is conceptually straightforward to extend our argument to higher dimensions. We will present this result in a forthcoming paper [45]. It will also be interesting to construct the crossing symmetric basis for conformal correlators of (external) spinning operators such as the energy-momentum tensor.…”

Section: Resultsmentioning

confidence: 92%

“…In this subsection we concentrate only on the three-dimensional case. A general dimensional version will be presented in a forthcoming paper [45].…”

Section: A2 Helicity Basismentioning

confidence: 99%

“…Our new basis manifests the analytic properties of conformal correlators. Also the connected and disconnected correlators are manifestly separated, so that it will be useful for the study of large N CFTs in particular.1 The results in general dimensions will be presented in [45].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Momentum space approach to crossing symmetric CFT correlators

Isono

Noumi

Shiu

2018

J. High Energ. Phys.

Self Cite

102

View full text Add to dashboard Cite

We construct a crossing symmetric basis for conformal four-point functions in momentum space by requiring consistent factorization. Just as scattering amplitudes factorize when the intermediate particle is on-shell, non-analytic parts of conformal correlators enjoy a similar factorization in momentum space. Based on this property, Polyakov, in his pioneering 1974 work, introduced a basis for conformal correlators which manifestly satisfies the crossing symmetry. He then initiated the bootstrap program by requiring its consistency with the operator product expansion. This approach is complementary to the ordinary bootstrap program, which is based on the conformal block and requires the crossing symmetry as a consistency condition of the theory. Even though Polyakov's original bootstrap approach has been revisited recently, the crossing symmetric basis has not been constructed explicitly in momentum space. In this paper we complete the construction of the crossing symmetric basis for scalar four-point functions with an intermediate operator with a general spin, by using new analytic expressions for three-point functions involving one tensor. Our new basis manifests the analytic properties of conformal correlators. Also the connected and disconnected correlators are manifestly separated, so that it will be useful for the study of large N CFTs in particular.

show abstract

Section: Resultsmentioning

confidence: 92%

“…In this subsection we concentrate only on the three-dimensional case. A general dimensional version will be presented in a forthcoming paper [45].…”

Section: A2 Helicity Basismentioning

confidence: 99%

See 1 more Smart Citation

Momentum space approach to crossing symmetric CFT correlators

Isono

Noumi

Shiu

2018

J. High Energ. Phys.

Self Cite

102

View full text Add to dashboard Cite

show abstract

“…Following the success of the conformal bootstrap program in position space (see [60,61] for reviews and [29][30][31][32][33] for related work), it may prove useful to develop a version in momentum space. This requires understanding the expansion of the tetrahedral integral W α,β in conformal partial waves [62][63][64][65].…”

Section: Discussionmentioning

confidence: 99%

“…These results are easy to derive in position space where the conformal group acts naturally. Yet for many modern applications, including cosmology [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], condensed matter [20][21][22][23][24][25], anomalies [26][27][28] and the bootstrap programme [29][30][31][32][33], it would be highly desirable to know the analogue of this result -and, indeed, the analogue of the conformal cross-ratios themselves -in momentum space.…”

mentioning

confidence: 99%

Conformal n -Point Functions in Momentum Space

2020

View full text Add to dashboard Cite

We provide a Feynman integral representation for the general momentum-space scalar n-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of n(n − 3)/2 variables which play the role of momentum-space conformal cross-ratios. It involves (n − 1)(n − 2)/2 integrations over momenta, with the momenta running over the edges of an (n−1)-simplex. Specializing to n = 4, we identify values of the operator and spacetime dimensions for which singularities arise leading to anomalies and beta functions.Several illustrative examples from perturbative quantum field theory and holography are discussed.

show abstract

Conformal correlators as simplex integrals in momentum space

Bzowski

McFadden

Skenderis

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We find the general solution of the conformal Ward identities for scalar n-point functions in momentum space and in general dimension. The solution is given in terms of integrals over (n − 1)-simplices in momentum space. The n operators are inserted at the n vertices of the simplex, and the momenta running between any two vertices of the simplex are the integration variables. The integrand involves an arbitrary function of momentum-space cross ratios constructed from the integration variables, while the external momenta enter only via momentum conservation at each vertex. Correlators where the function of cross ratios is a monomial exhibit a remarkable recursive structure where n-point functions are built in terms of (n − 1)-point functions. To illustrate our discussion, we derive the simplex representation of n-point contact Witten diagrams in a holographic conformal field theory. This can be achieved through both a recursive method, as well as an approach based on the star-mesh transformation of electrical circuit theory. The resulting expression for the function of cross ratios involves (n − 2) integrations, which is an improvement (when n > 4) relative to the Mellin representation that involves n(n − 3)/2 integrations.

show abstract

Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension

Cited by 58 publications

References 43 publications

Momentum space approach to crossing symmetric CFT correlators

Momentum space approach to crossing symmetric CFT correlators

Conformal n -Point Functions in Momentum Space

Conformal correlators as simplex integrals in momentum space

Contact Info

Product

Resources

About