Lattice supersymmetry, superfields and renormalization

TL;DR

This paper develops a superfield formalism for lattice supersymmetric models, enabling the construction of actions with preserved supersymmetries and demonstrating conditions for finiteness and correct continuum limits without fine tuning.

Contribution

It introduces a superfield approach to formulate and analyze lattice supersymmetric theories, ensuring exact supersymmetry and finiteness in the continuum limit.

Findings

Superfield formalism allows enumeration of all lattice supersymmetry invariants.

Some models preserve supersymmetry exactly, ensuring finiteness.

Continuum limit achieved without fine tuning in certain cases.

Abstract

We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent anticommuting supersymmetries. We introduce a superfield formalism, which allows the enumeration of all possible lattice supersymmetry invariants. We use it to discuss the formulation of Q-exact lattice actions and their renormalization in a general manner. In some examples, one exact supersymmetry guarantees finiteness of the continuum limit of the lattice theory. As a consequence, we show that the desired quantum continuum limit is obtained without fine tuning for these models. Finally, we discuss the implications and possible further applications of our results to the study of gauge and non-gauge models.