Boundary conditions for scalars in Lifshitz

Understand

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.