Conformal 
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-Point Functions in Momentum Space

Bzowski, Adam; McFadden, Paul; Skenderis, Kostas

doi:10.1103/physrevlett.124.131602

Cited by 77 publications

(75 citation statements)

References 76 publications

(126 reference statements)

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“…(1.1) in Minkowski space. Our work differs from most of the existing literature on 4-point functions in Euclidean momentum space [16][17][18], as well as other approaches to the conformal bootstrap in momentum space that are based on the existence of crossing-symmetric correlators [19][20][21].…”

Section: Introductionmentioning

confidence: 91%

Convergent momentum-space OPE and bootstrap equations in conformal field theory

Gillioz

Luty

et al. 2020

J. High Energ. Phys.

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General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.

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Section: Introductionmentioning

confidence: 91%

Convergent momentum-space OPE and bootstrap equations in conformal field theory

Gillioz

Luty

et al. 2020

J. High Energ. Phys.

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“…Furthermore, solving the special conformal Ward identity is in general hard as they are complicated second order differential equations in momentum variables. For specific higher point correlators limited progress has been made [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Despite the difficulties it is desirable to understand CFT in momentum space.…”

Section: Introductionmentioning

confidence: 99%

Momentum space spinning correlators and higher spin equations in three dimensions

Jain

John

Malvimat

2020

J. High Energ. Phys.

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In this article, we explicitly compute in momentum space the three and four-point correlation functions involving scalar and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the five-point function of the scalar operator in the free bosonic theory. We discuss techniques which are more efficient than the usual PV reduction to evaluate one loop integrals. Our techniques can be easily generalised to momentum space correlators of complicated spinning operators and to higher point functions. The three dimensional fermionic theory has the interesting feature that the scalar operator $$ \overline{\psi}\psi $$ ψ ¯ ψ is odd under parity. To account for this, we develop a parity odd basis which is useful to write correlation functions involving spinning operators and an odd number of $$ \overline{\psi}\psi $$ ψ ¯ ψ operators. We further study higher spin (HS) equations in momentum space which are algebraic in nature and hence simpler than their position space counterparts. We use them to solve for three-point functions involving spinning operators without invoking conformal invariance. However, at the level of four-point functions, solving the HS equation requires additional constraints that come from conformal invariance and we could only verify that our explicit results solve the HS equation.

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“…It would be interesting to explore how this extends to higherpoint correlators in momentum space. A general solution to the conformal Ward identities for n-point scalar correlators in momentum space was recently proposed in [51], so it would be interesting to extend this to tensorial correlators and understand how to systematically compute their flat space limit. Note that the general solution in [51] can be written as a 3-loop Feynman integral so it is conceivable that the flat space limit is encoded in the leading singularity of this integral.…”

Section: Discussionmentioning

confidence: 99%

“…A general solution to the conformal Ward identities for n-point scalar correlators in momentum space was recently proposed in [51], so it would be interesting to extend this to tensorial correlators and understand how to systematically compute their flat space limit. Note that the general solution in [51] can be written as a 3-loop Feynman integral so it is conceivable that the flat space limit is encoded in the leading singularity of this integral. It may also be fruitful to look for double copy structure in the correlators derived from Witten diagrams of specific theories in the bulk such as bi-adjoint scalars, Yang-Mills, and Einstein gravity.…”

Section: Discussionmentioning

confidence: 99%

Double copy structure and the flat space limit of conformal correlators in even dimensions

Lipstein

McFadden

2020

Phys. Rev. D

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We analyze the flat space limit of 3-point correlators in momentum space for general conformal field theories in even spacetime dimensions, and show they exhibit a double copy structure similar to that found in odd dimensions. In even dimensions, the situation is more complicated because correlators contain branch cuts and divergences which need to be renormalized. We describe the analytic continuation of momenta required to extract the flat space limit, and show that the flat space limit is encoded in the leading singularity of a 1-loop triangle integral which serves as a master integral for 3-point correlators in even dimensions. We then give a detailed analysis of the renormalized correlators in four dimensions where the flat space limit of stress tensor correlators is controlled by the coefficients in the trace anomaly.

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Conformal n -Point Functions in Momentum Space

Cited by 77 publications

References 76 publications

Convergent momentum-space OPE and bootstrap equations in conformal field theory

Convergent momentum-space OPE and bootstrap equations in conformal field theory

Momentum space spinning correlators and higher spin equations in three dimensions

Double copy structure and the flat space limit of conformal correlators in even dimensions

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