Beauty and the twist: the Bethe ansatz for twisted Script N = 4 SYM

Abstract

It was recently shown that the string theory duals of certain deformations of the N = 4 gauge theory can be obtained by a combination of T-duality transformations and coordinate shifts. Here we work out the corresponding procedure of twisting the dual integrable spin chain and its Bethe ansatz. We derive the Bethe equations for the complete twisted N = 4 gauge theory at one and higher loops. These have a natural generalization which we identify as twists involving the Cartan generators of the conformal algebra. The underlying model appears to be a form of noncommutative deformation of N = 4 SYM.

The general Leigh-Strassler deformation and integrability

“…This way of creating supergravity duals was used in [22] to construct a three-parameter generalization of the β-deformed theory. The gauge theory dual to this supergravity solution was found in [22,18] for q = e iγ j with γ j real, corresponding to certain phase deformations in the Lagrangian. This gauge theory is referred to as twisted SYM, from which the β-deformed theory is obtained when all the γ j = β.…”

“…This gauge theory is referred to as twisted SYM, from which the β-deformed theory is obtained when all the γ j = β. The result is that the theory is integrable for any q = e iγ j with γ j real [18]. The general case with complex γ j is not integrable [17,19].…”

Bethe ansatz equations for general orbifolds of 𝒩 = 4 SYM

“…It seems that the higher loop techniques described in [26], [52] apply to the non-Abelian case as well. This would open a possibility of applying the existing powerful integrability techniques to the quiver gauge theories with reduced supersymmetry.…”

“…Representation matrix R(g) being diagonalized as in (55), this shift results in a mere phase factor σ A (g)σ B (g) −1 . Note that the twist field gets conjugated, g → hgh −1 ; and this conjugation compensates for the action of the horizontal cut owing to the invariance condition (52). Then the summation over the cut h results in the projection onto the S g -invariant subspace.…”

Deformed PP-waves from the Lunin-Maldacena background

“…This indicates that the integrable structures in the gauge theory and the string theory match. Further analysis of the relevant spin chain is given in [7]. For further recent insights into the gauge/string correspondence for these (and other) new examples see [8].…”