Q: Scalar Boundary Condition & U(1) Isometry - Lewkowycz & Maldacena

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SUMMARY

The discussion centers on the boundary conditions for scalar fields in the BTZ (Banados-Teitelboim-Zanelli) background as presented in Lewkowycz and Maldacena's paper (arXiv:1304.4926v2). It establishes that the boundary condition $\phi \sim e^{i\tau}$ violates the U(1) isometry of the BTZ background. The key conclusion is that to maintain U(1) symmetry, the scalar field $\phi$ must be independent of the $\tau$ coordinate.

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  • Understanding of scalar fields in theoretical physics
  • Familiarity with the BTZ black hole background
  • Knowledge of U(1) symmetry in quantum field theory
  • Basic grasp of boundary conditions in field theory
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The discussion is beneficial for theoretical physicists, particularly those focusing on quantum field theory, black hole physics, and the study of symmetries in gravitational contexts.

craigthone
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I have a simple question about Lewkowycz and Maldacena's paper [PLAIN]http://arxiv.org/abs/1304.4926v2[/PLAIN]
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$?
 
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The answer is YES. Respecting U(1) symmetry of phi means independence of tau coordinate.
 

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