SUSY Ward identities, Superamplitudes, and Counterterms

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".

33 pages. Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories." v2: references added

References in corpus (21)

• Three-Loop Superfiniteness of N=8 Supergravity
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• E7(7) constraints on counterterms in N=8 supergravity
• Basics of Generalized Unitarity
• Ultraviolet properties of Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Generic multiloop methods and application to N=4 super-Yang-Mills
• The ultra-violet question in maximally supersymmetric field theories
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Supersymmetry Relations and MHV Amplitudes in Superstring Theory
• Modular properties of two-loop maximal supergravity and connections with string theory
• The footprint of E7 in amplitudes of N=8 supergravity
• Complete Six-Gluon Disk Amplitude in Superstring Theory
• Tree-Level Formalism
• N=8 Supergravity 4-point Amplitudes
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• The Ultraviolet Finiteness of N=8 Supergravity
• On UV Finiteness of the Four Loop N=8 Supergravity

Cited by in corpus (18)

• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Basics of Generalized Unitarity
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Scattering amplitudes: the most perfect microscopic structures in the universe
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• An Introduction to On-shell Recursion Relations
• Constraining Higher Derivative Supergravity with Scattering Amplitudes
• Tree-Level Formalism
• One-loop four-graviton amplitudes in N=4 supergravity models
• On Higher Derivative Couplings in Theories with Sixteen Supersymmetries
• Leading and Subleading UV Divergences in Scattering Amplitudes for D=8 N=1 SYM Theory in All Loops
• Challenges of D=6 N=(1,1) SYM Theory
• Supersymmetric Massive Gravity
• On-shell Supersymmetry and higher-spin amplitudes
• Hidden U(N) Symmetry behind N=1 Superamplitudes
• String Theory from Maximal Supersymmetry