Hidden U(N) Symmetry behind N=1 Superamplitudes

TL;DR

This paper reveals a hidden U(N) symmetry in N=1 superamplitudes, using Young diagrams to classify operators and relate them to superamplitudes via supersymmetric Ward identities.

Contribution

It introduces a Young diagram approach to classify higher dimensional operators in N=1 supersymmetry and connects them to superamplitudes through a hidden U(N) symmetry.

Findings

Superamplitudes correspond to specific Young tableaux.

Operators are classified using U(N) tensor products and Young diagrams.

The method simplifies reading operators directly from Young tableaux.

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.