Are there really any AdS_2 branes in the euclidean (or not) AdS_3?

TL;DR

This paper investigates the existence of AdS_2 branes in Euclidean and non-Euclidean AdS_3 models, concluding they do not exist in certain models and exploring boundary conditions through analytical continuation.

Contribution

It demonstrates the non-existence of AdS_2 branes in specific WZNW models and analyzes boundary conditions via analytical continuation in the SL(2,R) model.

Findings

No AdS_2 branes found in H_3^+ and SL(2,R) models

Boundary branes with su(2) symmetry likely reside on AdS_3 boundary

Euclidean spacetime cannot realize certain boundary conditions

Abstract

We do not find any AdS_2 branes, neither in the H_3^+ WZNW model nor the SL(2,R) WZNW model. We then reexamine the case of the branes that possess a su(2) symmetry: we speculate that they would have to live on the boundary of AdS_3. This cannot be realized in an euclidean spacetime, but in the SL(2,R) WZNW model by analytical continuation.