New worldsheet formulae for conformal supergravity amplitudes

Abstract

We use 4d ambitwistor string theory to derive new worldsheet formulae for tree-level conformal supergravity amplitudes supported on refined scattering equations. Unlike the worldsheet formulae for super-Yang-Mills or supergravity, the scattering equations for conformal supergravity are not in general refined by MHV degree. Nevertheless, we obtain a concise worldsheet formula for any number of scalars and gravitons which we lift to a manifestly supersymmetric formula using four types of vertex operators. The theory also contains states with non-plane wave boundary conditions and we show that the corresponding amplitudes can be obtained from plane-wave amplitudes by applying momentum derivatives. Such derivatives are subtle to define since the formulae are intrinsically four-dimensional and on-shell, so we develop a method for computing momentum derivatives of spinor variables.

Unraveling conformal gravity amplitudes

“…More specifically, four-derivative theories generally include both regular planewave modes and unusual non-planewave modes that exhibit linear growth -the two are sometimes described as forming a dipole. Whether the non-planewave modes are acceptable asymptotic states for the S-matrix is an interesting question [132,137]; our partial analysis seems to suggest that these states can be considered even if amplitudes for such states may pick up a dependence on a constant auxiliary vector α µ . As the four-derivative off-shell propagators are of the form 1/p 4 , the factorization properties of amplitudes when internal lines go on-shell are somewhat delicate.…”

“…Historically, these amplitudes arose from the N = 4 twistor string theory as a conformal gravity "contamination" of N = 4 SYM in the multitrace sector [12] (see also refs. [129,137,146]). Although some hints were provided in Berkovits and Witten's original work, a Lagrangian formulation of the field theory from which these amplitudes originate has until now been lacking.…”

Double copy structure of CFT correlators

“…Hence, A 220 φR 2 is the only 3-point amplitude which can be obtained from combining Yang-Mills and the F 3 gluon amplitudes in four dimensions. Generalizations to higher points in the form of worldsheet formulas can be found in [52][53][54][55].…”

A Monte Carlo approach to the 4D scattering equations

“…We will also analyse the integrands for some specific theories. Integrands are currently known for Einstein gravity and Yang-Mills theory with any valid number of supersymmetries [21], and for graviton multiplets in N = 4 conformal supergravity [23]. The supersymmetry structure is encoded by a set of fermionic delta functions of the form δ N η l − r∈R ηr (lr) , which can be thought of as scattering equations for the Grassmann on-shell superspace variables.…”

“…We will refer to these equations as '4D scattering equations'. In recent work we extended this formalism to include N = 4 conformal supergravity [23].…”