Semi-classical Strings in Sasaki-Einstein Manifolds

TL;DR

This paper explores classical string solutions in AdS_5 x X^5 backgrounds where X^5 are Sasaki-Einstein manifolds, revealing limited solutions constrained by manifold parameters and highlighting energy dependence and BPS solutions.

Contribution

It provides new classical string solutions on Sasaki-Einstein manifolds and analyzes their energy relations and BPS conditions, expanding understanding of string dynamics in these geometries.

Findings

Limited acceptable solutions due to manifold constraints

Energy depends transcendently on parameters and momenta

Discussion of BPS solutions included

Abstract

We find point-like and classical string solutions on the AdS_5 x X^5, where X^5 are the 5-dimensional Sasaki-Einstein manifolds Ypq and Lpqr. The number of acceptable solutions is limited drastically in order to satisfy the constraints on the parameters and coordinates of the manifolds. The energy of the solutions depends on the parameters of the Sasaki-Einstein manifolds and on the conserved momenta transcendentally. A discussion on BPS solutions is presented as well.