Boundary conditions for scalars in Lifshitz

Tomas Andrade; Simon F. Ross

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

paper

Boundary conditions for scalars in Lifshitz

arXiv:1212.2572 · doi:10.1088/0264-9381/30/6/065009

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 $m_{B F}^{2} < m^{2} < m_{B F}^{2} + 1$ , 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.

19 pages, 6 figures, minor typos corrected, references added

Boundary conditions for scalars in Lifshitz

Abstract

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