scalar field in background with U(1) isometry

Question

Hello everyone,

I have a simple question about Lewkowycz and Maldacena's paper http://arxiv.org/abs/1304.4926v2.

In section 2, they consider the scalar field in BTZ background ground and require boundary condition of the scalar field,

$\phi \sim e^{i\tau}$ . This boudary condition breaks the U(1) isomentry of BTZ background. My question is what kinds of boudary condition will respect the U(1) isometry? phi does not depend on tau?

Answer 1

yes, the boundary scalar could have a non-trivial profile in the "x" direction but it shouldn't depend on tau.