Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals

Details Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals

2005-02-08

arxiv.org/abs/hep-th/0502086v4

JHEP 0505 (2005) 033

Physics

High Energy Physics

High Energy Physics - Theory

35 pages. V3: typos fixed

Scientific paper

10.1088/1126-6708/2005/05/033

We find the gravity dual of a marginal deformation of ${\cal N}=4$ super Yang Mills, and discuss some of its properties. This deformation is intimately connected with an $SL(2,R)$ symmetry of the gravity theory. The $SL(2,R)$ transformation enables us to find the solutions in a simple way. These field theory deformations, sometimes called $\beta$ deformations, can be viewed as arising from a star product. Our method works for any theory that has a gravity dual with a $U(1)\times U(1)$ global symmetry which is realized geometrically. These include the field theories that live on D3 branes at the conifold or other toric singularities, as well as their cascading versions.

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