One-loop spectroscopy of semiclassically quantized strings: bosonic sector

TL;DR

This paper advances the exact quantization of spinning string states by computing the one-loop partition function for specific semiclassical solutions, revealing solvable differential operators in the bosonic sector.

Contribution

It provides an exact analytical calculation of the one-loop partition function for coupled fluctuation modes in semiclassical string solutions, including the Landau-Lifshitz model and $AdS_5$ strings.

Findings

Exact one-loop partition function computed for two-spin string solutions.

Fluctuation operators are fourth-order with meromorphic coefficients, solvable exactly.

Results apply to bosonic fluctuations in $SU(2)$ and $AdS_5$ sectors.

Abstract

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 $AdS_5$ with an angular momentum $J$ in $S^5$. 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.