Boundary conditions for scalars in Lifshitz

TL;DR

This paper investigates scalar field boundary conditions in Lifshitz spacetimes, revealing a new UV instability for certain mass ranges and proposing implications for dual field theories.

Contribution

It introduces the concept of alternative boundary conditions for scalars in Lifshitz backgrounds and identifies a novel UV instability affecting the dual theory.

Findings

Alternative boundary conditions are normalizable for a wider mass range than in AdS.

A new UV instability occurs for scalar masses in a specific range.

The dual field theory is ill-defined where the instability appears.

Abstract

We consider the quantisation of scalar fields on a Lifshitz background, exploring the possibility of alternative boundary conditions, allowing the slow falloff mode to fluctuate. We show that the scalar field with alternative boundary conditions is normalizable for a larger range of masses than in the AdS case. However, we then find a new instability for alternative boundary conditions, implying that the range of masses where alternative boundary conditions define a well-behaved dual theory is $m_{BF}^2 < m^2 < m^2_{BF} +1$, analogously to the AdS case. The instability is of a novel type, with modes of arbitrarily large momentum which grow exponentially in time; it is therefore essentially a UV effect, and implies that the dual field theory is simply not defined where it appears. We discuss the interpretation in the dual field theory, and give a proposed lower bound on the dimension of scalar operators.