1106.1116 (V. Giangreco M. Puletti et al.)

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

V. Giangreco M. Puletti, T. Mansson

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.

View original: http://arxiv.org/abs/1106.1116