# Holomorphic Structure and Quantum Critical Points in Supersymmetric Lifshitz Field Theories

## TL;DR

This paper constructs supersymmetric Lifshitz field theories with holomorphic structures, revealing lines of quantum critical points with exact Lifshitz scale invariance and dimension-dependent critical exponents.

## Contribution

It introduces a general framework for supersymmetric Lifshitz theories with non-renormalizable superpotentials and analyzes their quantum critical behavior across multiple dimensions.

## Key findings

- Existence of lines of quantum critical points with Lifshitz scale invariance
- Dependence of dynamical critical exponent on coupling constants
- Holomorphic structure and non-renormalization properties of the superpotential

## Abstract

We construct supersymmetric Lifshitz field theories with four real supercharges in a general number of space dimensions. The theories consist of complex bosons and fermions and exhibit a holomorphic structure and non-renormalization properties of the superpotential. We study the theories in a diverse number of space dimensions and for various choices of marginal interactions. We show that there are lines of quantum critical points with an exact Lifshitz scale invariance and a dynamical critical exponent that depends on the coupling constants.