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

Oleg Lunin·Juan Maldacena
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Abstract

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 $β$ 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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Oleg Lunin, Juan Maldacena. 2005-05-13. Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals. https://doi.org/10.1088/1126-6708%2F2005%2F05%2F033

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