Abstract
We construct semi-classical string solutions of the Schrödinger Sch5 ×S5 spacetime, which is conjectured to be the gravity dual of a non-local dipole-deformed CFT. They are the counterparts of the giant magnon and spiky string solutions of the undeformed AdS5 × S5 to which they flow when the deformation parameter is turned off. They live in an S3 subspace of the five-sphere along the directions of which the B-field has non-zero components, having also extent in the Sch5 part of the metric. Finally, we speculate on the form of the dual field theory operators.
Highlights
For which the magnon solution was calculated in [22] and the non-commutative theories [23]
We construct semi-classical string solutions of the Schrodinger Sch5×S5 spacetime, which is conjectured to be the gravity dual of a non-local dipole-deformed CFT. They are the counterparts of the giant magnon and spiky string solutions of the undeformed AdS5 × S5 to which they flow when the deformation parameter is turned off
In this paper we have derived semi-classical string solutions living in the Schrodinger Sch5× S5 spacetime which is conjectured to be the gravity dual of the non-local CFT coming under the name null dipole CFT
Summary
Applying the ansatz (2.4) on the equation of motion that is coming from the variation of (A.1) along the direction V , we end up with an equation for the function Ty(y). The equation of motion coming from the variation of (A.1) along the direction T , written in terms of y, can be integrated once, providing Vy(y) in terms of θy(y) and constants as follows. The equations of motion coming from the variation of (A.1) along the directions ψ and φ (in terms of y) can be integrated to express Ψy(y) and Φy(y) in terms of θy(y) and constants as follows. The equation of motion coming from the variation of Z will give us the following constraint for the constant Z0. Substituting the expressions (2.6), (2.7), (2.8) & (2.9) into the first Virasoro constraint (A.3), we obtain the following expression for θy(y). Substituting the expressions (2.6), (2.7), (2.8), (2.9) and (2.11) into the second Virasoro constraint (A.3), we obtain the following algebraic relation.
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