One-loop spectroscopy of semiclassically quantized strings: bosonic sector

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.1

Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

“…Chapter 4 is based on [2] and exploits the analytical solution to the spectral problem of a type of fourth-order differential operators. This finds application in the exact evaluation of the semiclassical contributions to the one-loop energy of a class of two-spin spinning strings in AdS 5 × S 5 .…”

“…In addition to the Z 2 -grading implicit in the definition of superalgebra g -for whichg (0) ,g (2) are even andg (1) ,g (3) are odd subspaces -the automorphism endows g with the structure of a Z 4 -graded algebra [269].…”

“…2 Most of the discussion here is tailored to section 2.1.1. A primer on classical and quantum field theories with emphasis on modern AdS/CFT applications can be found in [63].…”

“…an integrability condition relating the worldsheet curvature (2) Rãcbd to the extrinsic and background geometry as characterized by the extrinsic curvature K Ã ab and the space-time…”

“…If we again eliminate the metric fluctuationḡ ij through its equation of motion, we get back to the mass matrix M (B) ij and to L (2) transv in (3.47).…”