Boundary conditions for scalars in Lifshitz

Andrade, Tomas; Ross, Simon F.

doi:10.1088/0264-9381/30/6/065009

Boundary conditions for scalars in Lifshitz

Andrade, Tomas; Ross, Simon F.

Authors

Tomas Andrade

Professor Simon Ross s.f.ross@durham.ac.uk
Professor

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.

Citation

Andrade, T., & Ross, S. F. (2013). Boundary conditions for scalars in Lifshitz. Classical and Quantum Gravity, 30(6), Article 065009. https://doi.org/10.1088/0264-9381/30/6/065009

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