Remarks on the geometrical properties of semiclassically quantized strings

TL;DR

This paper explores the geometric aspects of semiclassical string quantization in AdS5 x S5, focusing on fluctuations around classical solutions and deriving compact spectral formulas for bosonic and fermionic modes.

Contribution

It introduces geometric invariants to express fluctuation operators and provides explicit examples like spinning strings and Wilson loops to illustrate the approach.

Findings

Derived compact spectral formulas for fluctuations

Analyzed geometric structures on fluctuation bundles

Explicitly applied methods to spinning string and Wilson loop

Abstract

We discuss some geometrical aspects of the semiclassical quantization of string solutions in Type IIB Green-Schwarz action on $\ads_5\times \sphere^5$. We concentrate on quadratic fluctuations around classical configurations, expressing the relevant differential operators in terms of (intrinsic and extrinsic) invariants of the background geometry. The aim of our exercises is to present some compact expressions encoding the spectral properties of bosonic and fermionic fluctuations. The appearing of non-trivial structures on the relevant bundles and their role in concrete computations are also considered. We corroborate the presentation of general formulas by working out explicitly a couple of relevant examples, namely the spinning string and the latitude BPS Wilson loop.