One-loop spectroscopy of semiclassically quantized strings: Bosonic sector

We make a further step in the analytically exact quantization of spinning string states in semiclassical approximation, by evaluating the exact one-loop partition function for a class of two-spin string solutions for which quadratic fluctuations form a non-trivial system of coupled modes. This is the case of a folded string in the SU(2) sector, in the limit described by a quantum Landau-Lifshitz model. The same applies to the full bosonic sector of fluctuations over the folded spinning string in AdS₅ with an angular momentum J in S⁵. Fluctuations are governed by a special class of fourth-order differential operators, with coefficients being meromorphic functions on the torus, which we are able to solve exactly.