Power-counting and Renormalizability in Lifshitz Scalar Theory

TL;DR

This paper investigates the renormalizability of Lifshitz scalar theories, showing that symmetries like shift symmetry can ensure finiteness in counter terms, which is crucial for consistent matter sectors in Horava-Lifshitz gravity.

Contribution

It demonstrates how shift symmetry can control counter terms in Lifshitz scalar theories, improving their renormalizability prospects.

Findings

Power-counting holds at one-loop order.

Without symmetries, infinite counter terms are needed.

Shift symmetry restricts counter terms to a finite set.

Abstract

We study the renormalizability in theories of a self-interacting Lifshitz scalar field. We show that although the statement of power-counting is true at one-loop order, in generic cases where the scalar field is dimensionless, an infinite number of counter terms are involved in the renormalization procedure. This problem can be avoided by imposing symmetries, the shift symmetry in the present paper, which allow only a finite number of counter terms to appear. The symmetry requirements might have important implications for the construction of matter field sectors in the Horava-Lifshitz gravity.