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Operator Renormalization using Emergent Supersymmetries

Mrigankamauli Chakraborty, Sven-Olaf Moch

Abstract

We develop a mechanism that enables supersymmetric Ward identities to be applied in non-supersymmetric theories. These identities are then used to streamline calculations in our target theories, potentially including phenomenological models. In these proceedings, we illustrate the method through operator renormalization in the Gross-Neveu-Yukawa model, where it leads to a significant optimization and a substantial reduction in computational effort. This serves as a toy example of the procedure that we ultimately aim to apply to Quantum Chromodynamics.

Operator Renormalization using Emergent Supersymmetries

Abstract

We develop a mechanism that enables supersymmetric Ward identities to be applied in non-supersymmetric theories. These identities are then used to streamline calculations in our target theories, potentially including phenomenological models. In these proceedings, we illustrate the method through operator renormalization in the Gross-Neveu-Yukawa model, where it leads to a significant optimization and a substantial reduction in computational effort. This serves as a toy example of the procedure that we ultimately aim to apply to Quantum Chromodynamics.
Paper Structure (5 sections, 1 theorem, 12 equations, 1 figure)

This paper contains 5 sections, 1 theorem, 12 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Generalised Lagrangian
  3. Emergent SUSY in $\mathcal{L}^{\text{gen}}$
  4. Using emergent SUSY to optimize calculations in GNY
  5. Summary and future outlook

Key Result

Theorem 1

There are no evanescent flavour terms in the generalised Lagrangian $\mathcal{L}^{\text{gen}}$ if and only if the $Z,\bar{Z}$ satisfy the following relation: i.e. the same relation satisfied by the Pauli matrices $\sigma^\mu,\bar{\sigma}^\mu$.

Figures (1)

  • Figure 1: Plot of the SUSY Ward Identity $\gamma_f=\gamma_s$ at every loop order up to 4 loops, y-axis is $n_s$, x-axis is $n_f$. Curves for every loop order intersect at the same 2 points, signifying that $\mathcal{L}^{\text{gen}}$ as a whole becomes supersymmetric at those two points.

Theorems & Definitions (1)

  • Theorem 1