SUSY Ward identities, Superamplitudes, and Counterterms

TL;DR

This paper reviews how SUSY and R-symmetry Ward identities relate superamplitudes and constrain counterterms in supersymmetric theories like N=4 SYM and N=8 supergravity, providing a basis for analyzing ultraviolet divergences.

Contribution

It presents a comprehensive solution to Ward identities at tree and loop levels, expressing superamplitudes in terms of basis amplitudes classified by Young diagrams, and introduces a matrix element approach to counterterms.

Findings

Superamplitudes are expressed via basis amplitudes classified by Young diagrams.

Ward identities impose constraints on counterterm matrix elements.

The approach offers a systematic way to analyze ultraviolet divergences.

Abstract

Ward identities of SUSY and R-symmetry relate n-point amplitudes in supersymmetric theories. We review recent work in which these Ward identities are solved in N=4 SYM and N=8 supergravity. The solution, valid at both tree and loop level, expresses any (Next-to)^K MHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard tableaux of rectangular N-by-K Young diagrams. The SUSY Ward identities also impose constraints on the matrix elements of candidate ultraviolet counterterms in N=8 supergravity, and they can be studied using superamplitude basis expansions. This leads to a novel and quite comprehensive matrix element approach to counterterms, which we also review. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".