Open String Fluctuations in AdS with and without Torsion

TL;DR

This paper develops a covariant formalism for analyzing fluctuations of open strings in curved spacetimes with torsion, demonstrating finiteness of physical fluctuations at boundaries and applicability to AdS/CFT contexts.

Contribution

It introduces a covariant approach to string fluctuations in torsioned backgrounds and analyzes boundary behavior, extending to both open and closed strings in AdS spaces.

Findings

Physical fluctuations remain finite at the boundary despite world-sheet singularities.

The formalism applies to both open and closed strings in AdS spaces.

Divergences in 2-curvature are less problematic than previously thought.

Abstract

The equations of motion and boundary conditions for the fluctuations around a classical open string, in a curved space-time with torsion, are considered in compact and world-sheet covariant form. The rigidly rotating open strings in Anti de Sitter space with and without torsion are investigated in detail. By carefully analyzing the tangential fluctuations at the boundary, we show explicitly that the physical fluctuations (which at the boundary are combinations of normal and tangential fluctuations) are finite, even though the world-sheet is singular there. The divergent 2-curvature thus seems less dangerous than expected, in these cases. The general formalism can be straightforwardly used also to study the (bosonic part of the) fluctuations around the closed strings, recently considered in connection with the AdS/CFT duality, on AdS_5 \times S^5 and AdS_3 \times S^3 \times T^4.