Hidden U(N) Symmetry behind N=1 Superamplitudes

Abstract

In this paper we develop a Young diagram approach to constructing higher dimensional operators formed from massless superfields and their superderivatives in $\mathcal{N}=1$ supersymmetry. These operators are in one-to-one correspondence with non-factorizable terms in on-shell superamplitudes, which can be studied with massless spinor helicity techniques. By relating all spin-helicity variables to certain representations under a hidden $U(N)$ symmetry behind the theory, we show each non-factorizable superamplitude can be identified with a specific Young tableau. The desired tableau is picked out of a more general set of $U(N)$ tensor products by enforcing the supersymmetric Ward identities. We then relate these Young tableaux to higher dimensional superfield operators and list the rules to read operators directly from Young tableau. Using this method, we present several illustrative examples.

arXiv comment29 pages, 10 figures

References in corpus (21)

• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• What is the Simplest Quantum Field Theory?
• Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
• On-shell constructibility of tree amplitudes in general field theories
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory
• Solution to the Ward Identities for Superamplitudes
• Operator Bases in Effective Field Theories with Sterile Neutrinos: $d\le 9$
• On-shell superamplitudes in N<4 SYM
• Standard Model Effective Field Theory from On-shell Amplitudes
• Constructing effective field theories via their harmonics
• The Rise of SMEFT On-shell Amplitudes
• Constructing massive on-shell contact terms
• Low Energy Effective Field Theory Operator Basis at $d\le 9$
• Standard Model Effective Field Theory up to Mass Dimension 12
• An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes
• SUSY Ward identities, Superamplitudes, and Counterterms
• On-shell supersymmetry for massive multiplets
• Massive On-Shell Supersymmetric Scattering Amplitudes
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
• Counting Operators in $N=1$ Supersymmetric Gauge Theories

Cited by in corpus (1)

• Basis for Non-Factorizable Superamplitudes in N = 1 Supersymmetry