Gauge-string duality for superconformal deformations ofN= 4 Super Yang-Mills theory

Abstract

We analyze in detail the relation between an exactly marginal deformation of N = 4 SYM -the Leigh-Strassler or "β-deformation" -and its string theory dual (recently constructed in hep-th/0502086) by comparing energies of semiclassical strings to anomalous dimensions of gauge-theory operators in the two-scalar sector. We stress the existence of integrable structures on the two sides of the duality. In particular, we argue that the integrability of strings in AdS 5 × S 5 implies the integrability of the deformed world sheet theory with real deformation parameter. We compare the fast string limit of the worldsheet action in the sector with two angular momenta with the continuum limit of the coherent state action of an anisotropic XXZ spin chain describing the one-loop anomalous dimensions of the corresponding operators and find a remarkable agreement for all values of the deformation parameter. We discuss some of the properties of the Bethe Ansatz for this spin chain, solve the Bethe equations for small number of excitations and comment on higher loop properties of the dilatation operator. With the goal of going beyond the leading order in the 't Hooft expansion we derive the analog of the Bethe equations on the string-theory side, and show that they coincide with the thermodynamic limit of the Bethe equations for the spin chain. We also compute the 1/J corrections to the anomalous dimensions of operators with large R-charge (corresponding to strings with angular momentum J) and match them to the 1-loop corrections to the fast string energies. Our results suggest that the impressive agreement between the gauge theory and semiclassical strings in AdS 5 × S 5 is part of a larger picture underlying the gauge/gravity duality.

The anatomy of gauge/string duality in Lunin-Maldacena background

“…To be more detailed, one usually seeks the solitonic solutions to the classical string sigma model lently Lunin-Maldacena background was done in [32,34] (For some earlier work, see [35,36]), where various techniques used for the maximally supersymmetric theory were extended and generalized.…”

“…This part overlaps with the materials presented in [34], however we decide to keep it for completeness as well as being a good entry route for establishing the correspondence.…”

“…Section 3 is devoted to two explicit semi-classical string solutions with two spins in the Lunin-Maldacena background, using the action derived from section 2. In section 4, we present the detailed twisted spin-chain analysis partly based on the results in [34,38]. We also propose ansätz for the outlines of Bethe strings in the scaling limit.…”

String spectrum of curved string backgrounds obtained by T-duality and shifts of polar angles

“…The models are constructed by applying a T duality transformation, then a shift of a periodic coordinate, and then another T-duality transformation. These transformations were generally referred as TsT transformations in [12], and here we will adopt this name. In contrast to [1], where the shift involves an S 1 coordinate, in [11] the shift only involves polar angles.…”

Deformed PP-waves from the Lunin-Maldacena background

“…Motivated by this, semiclassical string states in the LM background were recently compared to a class of gauge theory scalar operators [5]. The 1-loop anomalous dimensions of these operators are described by an integrable spin chain and match beautifully with the energies of the semiclassical string states.…”