The dual string sigma-model of the SU_q(3) sector

TL;DR

This paper studies the superstring sigma-model of the marginally deformed SU_q(3) sector in N=4 SYM, showing that for rational spinning strings, the energy matches Bethe ansatz calculations, extending understanding of integrability in deformed theories.

Contribution

It provides the first supergravity analysis of the SU_q(3) sector for purely imaginary beta-deformations, connecting string energies with Bethe equations in the fast spinning limit.

Findings

Superstring sigma-model reproduces Bethe ansatz energies for rational strings.

Extends integrability results to the supergravity dual of the deformed SU_q(3) sector.

Shows consistency between string theory and gauge theory in the deformed setting.

Abstract

In four-dimensional N=4 super Yang-Mills (SYM) the SU(3) sub-sector spanned by purely holomorphic fields is isomorphic to the corresponding mixed one spanned by both holomorphic and antiholomorphic fields. This is no longer the case when one considers the marginally deformed N=4 SYM. The mixed SU(3) sector marginally deformed by a complex parameter beta, i.e. SU_q(3) with q=e^{2 i\pi\beta}, has been shown to be integrable at one-loop hep-th/0703150, while it is not the case for the corresponding purely holomorphic one. Moreover, the marginally deformed N=4 SYM also has a gravity dual constructed by Lunin and Maldacena in hep-th/0502086. However, the mixed SU_q(3) sector has not been studied from the supergravity point of view. Hence in this note, for the case of purely imaginary marginal $\beta$-deformations, we compute the superstring SU_q(3) \sigma-model in the fast spinning string limit and show that, for rational spinning strings, it reproduces the energy computed via Bethe equations.