Exact computation of one-loop correction to the energy of folded spinning string in AdS5 x S5

We consider the one-loop correction to the energy of the folded spinning string solution in the AdS(3) part ofAdS(5)xS(5). The classical string solution is expressed in terms of elliptic functions so an explicit computation of the corresponding fluctuation determinants for generic values of the spin appears to be a non-trivial problem. We show how it can be solved exactly by using the static-gauge expression for the string partition function (which we demonstrate to be equivalent to the conformal gauge one) and observing that all the corresponding second-order fluctuation operators can be put into the standard (single-gap) Lame form. We systematically derive the small-spin and large-spin expansions of the resulting expression for the string energy and comment on some of their applications.