On the non-BPS string solutions in Sasaki-Einstein gauge/gravity duality

TL;DR

This paper analyzes non-BPS string solutions in Sasaki-Einstein manifolds within AdS_5 x Ypq, revealing how their energy relates to manifold parameters and identifying conditions under which they approach BPS states.

Contribution

It provides a detailed study of energy-spin relations for string solutions in Ypq manifolds, highlighting conditions for BPS limits and the influence of manifold parameters.

Findings

Energy depends on the parameter a(p,q) of the manifold.

Some solutions approach BPS energy at parameter limits.

Certain non-BPS solutions become BPS in specific manifolds.

Abstract

We present an extensive analysis on several string solutions in AdS_5 x Ypq and find some interesting properties of their energy-spin relations. Their energy depends always on the parameter a(p,q) which characterizes these manifolds. The range of this parameter for the string solutions is constrained by the Sasaki-Einstein constraints that the solutions should satisfy. Hence some string solutions we find are not valid for the whole class of Ypq manifolds. For some of our solutions, when the maximum allowed value of a(p,q) corresponds to the string approaching the poles of the squashed sphere in Ypq, their energy at this limit approaches the BPS one. Thus certain non-BPS string solutions in the whole class of Sasaki-Einstein manifolds, can become BPS in particular manifolds. For the solutions with this property we point out that this behavior is independent of the string motion in the other directions on the manifold. We expect that in the field theory the corresponding generic operators to these semi-classical strings, become BPS at certain quivers.