String Quantization in Curved Spacetimes: Null String Approach

TL;DR

This paper develops a systematic approach to quantize strings in curved spacetimes, focusing on null strings and their behavior in de Sitter space, revealing insights into string dynamics without critical dimension constraints.

Contribution

It introduces a novel expansion method for quantum strings in curved backgrounds, analyzing null strings and their first-order corrections in de Sitter spacetime.

Findings

Null string limit obtained at zeroth order.

First order corrections incorporate string dynamics.

No critical dimension constraint found.

Abstract

We study quantum strings in strong gravitational fields. The relevant small parameter is $g=R_c{\sqrt T_0}$, where $R_c$ is the curvature of the spacetime and $T_0$ is the string tension. Within our systematic expansion we obtain to zeroth order the null string (string with zero tension), while the first order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the world-sheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated however that the conformal anomaly will appear when the first order corrections proportional to $T_0$, are introduced.