Connecting Supersymmetry to Non-Supersymmetric theories: the Gross-Neveu-Yukawa example

TL;DR

This paper unifies several quantum field theories into a single framework, clarifying how supersymmetry can emerge at critical points and simplifying complex calculations.

Contribution

It introduces a generalized Lagrangian connecting multiple models, revealing structural links and enabling easier loop calculations in both supersymmetric and non-supersymmetric theories.

Findings

Unified framework clarifies emergence of supersymmetry at critical points

Additional Ward identities simplify loop calculations

Reduces computational cost for anomalous dimensions of operators

Abstract

We construct a generalized Lagrangian that unifies the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models, allowing for arbitrary scalar and fermion flavors in $D$-dimensional regularization. This framework clarifies how emergent supersymmetry arises at critical points and reveals structural connections between these theories. The unified formulation provides additional supersymmetry Ward identities that simplify loop calculations, even for non-supersymmetric models. As an application, we show how this technique can reduce the computational cost of determining anomalous dimensions of twist-two operators.