Boundary conditions for scalars in Lifshitz

Andrade, Tomas; Ross, Simon F.

Abstract

We consider the quantization 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 m2BF < m2 < m2BF + 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.

• Journal Article Type: Article
• Publication Date: Mar 1, 2013
• Deposit Date: Sep 6, 2013
• Publicly Available Date: Dec 21, 2013
• Journal: Classical and Quantum Gravity
• Print ISSN: 0264-9381
• Electronic ISSN: 1361-6382
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 30
• Issue: 6
• Article Number: 065009
• DOI: https://doi.org/10.1088/0264-9381/30/6/065009
• Public URL: https://durham-repository.worktribe.com/output/1478629