Energy Positivity, Non-Renormalization, and Holomorphy in Lorentz-Violating Supersymmetric Theories

TL;DR

This paper demonstrates that core supersymmetry properties like positive energy and non-renormalization persist even when Lorentz-violating interactions are introduced, using holomorphic and non-renormalization arguments.

Contribution

It extends supersymmetry theorems to Lorentz-violating theories, showing conditions for energy positivity and superpotential non-renormalization.

Findings

Positive-energy theorems hold with Lorentz violation under certain constraints.

Superpotential remains non-renormalized perturbatively despite Lorentz-violating interactions.

Holomorphy arguments provide elegant proofs of non-renormalization in Lorentz-violating supersymmetric theories.

Abstract

This paper shows that the positive-energy and non-renormalization theorems of traditional supersymmetry survive the addition of Lorentz violating interactions. The Lorentz-violating coupling constants in theories using the construction of Berger and Kostelecky must obey certain constraints in order to preserve the positive energy theorem. Seiberg's holomorphic arguments are used to prove that the superpotential remains non-renormalized (perturbatively) in the presence of Lorentz-violating interactions of the Berger-Kostelecky type. We briefly comment on Lorentz-violating theories of the type constructed by Nibbelink and Pospelov to note that holomorphy arguments offer elegant proofs of many non-renormalization results, some known by other arguments, some new.