Unraveling conformal gravity amplitudes

124

119

We consider the momentum-space 3-point correlators of currents, stress tensors and marginal scalar operators in general odd-dimensional conformal field theories. We show that the flat space limit of these correlators is spanned by gauge and gravitational scattering amplitudes in one higher dimension which are related by a double copy. Moreover, we recast three-dimensional CFT correlators in terms of tree-level Feynman diagrams without energy conservation, suggesting double copy structure beyond the flat space limit.

Section: Contentsmentioning

confidence: 88%

Double copy structure of CFT correlators

Farrow

Lipstein

McFadden

2019

124

119

“…Despite this, they are of interest for a few reasons. Namely, one type of conformal gravity arises in Berkovits-Witten twistor string [31], it is the zero-mass limit of a mass-deformed theory that reproduces Einstein gravity in the infinite-mass limit [32], and it may be useful for computing Einstein gravity amplitude in curved backgrounds for cosmological applications [33,34].…”

Section: Analytical Reconstructionmentioning

confidence: 99%

“…2.18) given in Ref. [32], where the derivative is implicit in the fact that we have to take the zero mass limit of expressions like (A L (m 2 )−A L (0))/m 2 . This would also explain why our approach fails: the amplitudes we use are well defined only exactly at the factorisation point, where the legs are on-shell and massless.…”

Section: Conformal Gravity: Nmhv (Partial)mentioning

confidence: 99%

Analytical amplitudes from numerical solutions of the scattering equations

Laurentis

2020

The CHY formalism for massless scattering provides a cohesive framework for the computation of scattering amplitudes in a variety of theories. It is especially compelling because it elucidates existing relations among theories which are seemingly unrelated in a standard Lagrangian formulation. However, it entails operations that are highly non-trivial to perform analytically, most notably solving the scattering equations. We present a new Python package (seampy) to solve the scattering equations and to compute scattering amplitudes. Both operations are done numerically with high-precision floating-point algebra. Elimination theory is used to obtain solutions to the scattering equations for arbitrary kinematics. These solutions are then applied to a variety of CHY integrands to obtain tree amplitudes for the following theories: Yang-Mills, Einstein gravity, biadjoint scalar, Born-Infeld, non-linear sigma model, Galileon, conformal gravity and (DF) 2 . Finally, we exploit this high-precision numerical implementation to explore the singularity structure of the amplitudes and to reconstruct analytical expressions which make manifest their pole structure. Some of the expressions for conformal gravity and the (DF) 2 gauge theory are new to the best of our knowledge.

“…12 The field content includes the 4-derivative gauge field A m , the 3-derivative 6d Weyl spinor Ψ, and the three 2-derivative real scalars Φ I (I = 1, 2, 3). 13 In total, one has 9 + 3 bosonic and 3 × 4 fermionic on-shell degrees of freedom (for each value of the internal index).…”

Section: (10) Supersymmetric Theorymentioning

confidence: 99%

“…12 This can be easily understood using, e.g., the standard N = 1 4d superspace formulation: the YM field strength Fmn is part of the spinor superfield strength Wα and thus constructing an invariant cubic in Wα is not possible. 13 In the case of the standard (1,0) SYM theory (corresponding to N = 2 SYM theory in 4d) the latter correspond to the auxiliary scalars. 14 Our notation differ significantly from that of [5] (where, e.g., the scalar kinetic term is defined using ǫ ij to raise the indices and thus implicitly is negative definite We suppressed interactions that are more than second order in the scalars and fermions, as they will not contribute to the one-loop divergences in a gauge-field background.…”

Section: (10) Supersymmetric Theorymentioning

confidence: 99%

One-loop β-functions in 4-derivative gauge theory in 6 dimensions

Casarin

Tseytlin

2019

A classically scale-invariant 6d analog of the 4d Yang-Mills theory is the 4-derivative (∇F ) 2 + F 3 gauge theory with two independent couplings. Motivated by a search for a perturbatively conformal but possibly non-unitary 6d models we compute the one-loop β-functions in this theory. A systematic way of doing this using the background field method requires the (previously unknown) expression for the b 6 Seeley-DeWitt coefficient for a generic 4-derivative operator; we derive it here. As an application, we also compute the one-loop β-function in the (1,0) supersymmetric (∇F ) 2 6d gauge theory constructed in hep-th/0505082. 1 lorenzo.casarin@aei.mpg.de 2 Also at the Lebedev Institute, Moscow. tseytlin@imperial.ac.uk 1 In 4 dimensions the F 2 + (∇F ) 2 + F 3 theory was studied in [2] and later in [3]. The result of [2] for the one-loop divergences in this 4d theory was corrected in [4] making it in agreement with that of [3].2 We use m, n, k, ... = 1, ..., 6 for coordinate indices and flat Euclidean 6d metric so that the position of contracted indices is irrelevant. The gauge group generators are normalized as tr(t a t b ) = −TRδ ab , [t a , t b ] = f abc t c , where TR = 1 2 in the fundamental representation of SU (N ) (we denote the trace in this case as Tr) and TR = C2 = N in the adjoint representation.3 Two other possible 4-derivative ∇F ∇F invariants are related to the above two by the Bianchi identity, e.g.,Fmn∇ 2 Fmn = −2 (∇mFmn) 2 + 4FmnF nk F km + total derivative. 4 Here tr is the trace over the matrix indices of a particular representation to which the quantum field belongs;for example, in the gauge theory case it is in the adjoint representation A ab m = f acb A c m , f acd f bcd = C2δ ab .