Constraints on Higher Derivative Operators in the Matrix Theory Effective Lagrangian

TL;DR

This paper investigates the non-renormalization properties of higher derivative operators in the Matrix theory effective Lagrangian, focusing on supersymmetry constraints for SU(N_c) groups beyond SU(2).

Contribution

It extends non-renormalization theorems to SU(N_c) groups with N_c>2, identifying which tensor structures are protected by supersymmetry.

Findings

Non-renormalization theorems proven for certain tensor structures.

Some tensor structures may be renormalized at three loops or higher.

Constraints from supersymmetry limit renormalization of specific terms.

Abstract

The consistency of Matrix theory with supergravity requires that in the large N_c limit terms of order v^4 in the SU(N_c) Matrix effective potential are not renormalized beyond one loop in perturbation theory. For SU(2) gauge group, the required non-renormalization theorem was proven recently by Paban, Sethi and Stern. In this paper we consider the constraints supersymmetry imposes on these terms for groups SU(N_c) with N_c>2. Non-renormalization theorems are proven for certain tensor structures, including the structures that appear in the one-loop effective action. However it is expected other tensor structures can in general be present, which may suffer renormalization at three loops and beyond.