String theory dual of the β-deformed gauge theory

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, β → β + 1 and β → β + τ 0 , to match the β-periodicity property of the dual gauge theory. Secondly, we reconcile the SL(2, Z) symmetry of the gauge theory, which acts on the constant parameters τ 0 and β, with the SL(2, Z) invariance of the string theory, which involves the dilaton-axion field τ (x). Our proposed modified configuration transforms correctly under the SL(2, Z) of string theory when its parameters are transformed under the SL(2, Z) 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.

Instanton test of non-supersymmetric deformations of theAdS5×S5

“…We note that this semi-classical field theory result is valid for any value of the parameters γ i and, as such, can be interpreted [16] as a (weak-coupling) prediction for the τ field in the exact string theory background. The supergravity regime is reached in the limit of γ i 1 which gives:…”

“…Much has been learnt recently about the gauge theory -string theory duality by investigating how the AdS/CFT correspondence [1] is realised when the N = 4 supersymmetric gauge theory is deformed by exactly marginal operators [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Since the gauge theory stays conformal it is expected to be dual (in the appropriate limit) to a supergravity solution with Anti-de Sitter geometry.…”

The Leigh-Strassler deformation and the quest for integrability

“…One way to start an exploration is to consider the string background in [13,19] for the q-deformed case, but the background there seems only valid for q close to one. In another article, some changes were suggested that could possibly extend the validity to arbitrary q values [38].…”

Integrable twists in AdS/CFT

“…It is possible that in the non-supersymmetric deformation the so(6) bosons do not form a closed subsector but mix with the fermions. Another possibility is that the background itself needs to be corrected, perhaps along the lines of [76]. It is also interesting that the nonsupersymmetric deformation is unstable due to the flow of double trace couplings [77], similar to the case found for orbifolds of N = 4 SYM [78,79].…”