Gauge - string duality for superconformal deformations of N =
4 super Yang-Mills theory
JHEP, (2005)Abstract
We analyze in detail the relation between an exactly marginal deformation
of N=4 SYM - the Leigh-Strassler or ``beta-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 x 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 x S^5 is part of a larger picture underlying the
gauge/gravity duality.