Abstract
We consider the AdS/CFT correspondence between the β-deformed supersymmetric gauge theory and the type IIB string theory on the Lunin-Maldacena background. Guided by gauge theory results, we modify and extend the supergravity solution of Lunin and Maldacena in two ways. First we make it to be doubly periodic in the deformation parameter, ββ+1 and ββ+τ 0 , to match the β-periodicity property of the dual gauge theory. Secondly, we reconcile the SL(2,) symmetry of the gauge theory, which acts on the constant parameters τ 0 and β, with the SL(2,) invariance of the string theory, which involves the dilaton-axion field τ(x). Our proposed modified configuration transforms correctly under the SL(2,) of string theory when its parameters are transformed under the SL(2,) of the gauge theory. We interpret the resulting configuration as the string theory (rather than supergravity) background which is dual to the β-deformed conformal Yang-Mills. Finally, we check that our string theory background leads to the IIB effective action which is correctly reproduced by instanton calculations on the gauge theory side, carried out at weak coupling, in the large-N limit, but to all orders in the deformation parameter β. © SISSA 2006.