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

Abstract

We present an extensive analysis on several string solutions in AdS 5 × Y p,q 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 Y p,q 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 Y p,q , 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.

Non-integrability in non-relativistic theories

“…The string solutions again show chaotic behavior implying nonintegrability of the corresponding sigma models. However, in Y p,q manifolds special care should be taken with the string solution to show that indeed they satisfy the Sasaki-Einstein constraints as in [15,16,17]. More recently it has been shown that integrability is not present in marginal complex β-deformations [18].…”

Generalised cusp anomalous dimension in β−deformed super Yang Mills theory

“…This implies that the system of equations (28), (29) and (34) becomes the same as the corresponding system of equations in the undeformed theory N = 4 sYM but with the redefined angle ∆θ ef f in the place of the angle ∆θ S 5 , where in the undeformed theory ∆θ S 5 is the angle of the cusp in the internal space. Calculating the expression for the quark anti-quark potential in the deformed theory we see that it depends only on y 1 and the turning point of the string y 2 and not on c 1 andγ explicitly.…”

Semiclassical strings in marginally deformed toric AdS/CFT

“…This value of y leads to important simplifications and although this is a limiting example, since it is a very special point in our manifold we examine if the full solution exist for completeness. The third equation of (22) and the last equation of (23) using the fact that J α = 0 giveṡ…”

“…It turns outs that the equations (22) and the last equation of (23) are satisfied as well as the first equation of motion (60). The equation (61) however introduces a relation between the deformation parameterγ and the coordinate y, and this implies that a BPS string solution for a fixed deformation parameterγ, exist only in a particular Sasaki-Einstein manifold.…”

“…Similar analysis applied to the generalized spaces with cohomogeneity two, called L p,q,r [28], in [20]. More recently, it has been done an extended analysis of the non-BPS string solutions in these backgrounds [21,22]. A discussion on the pulsating strings is presented in [23].…”