The Euler characteristic and the first Chern number in the covariant phase space formulation of string theory

TL;DR

This paper investigates how topological invariants like the Euler characteristic and the first Chern number influence the symplectic structure of string theory's covariant phase space, without affecting the string's dynamics.

Contribution

It introduces a covariant geometric framework to analyze topological corrections in string theory, highlighting their impact on the phase space structure.

Findings

Topological terms modify the symplectic form of the covariant phase space.

These corrections do not alter the classical equations of motion.

The approach provides a basis for future extensions in string theory analysis.

Abstract

Using a covariant description of the geometry of deformations for extendons, it is shown that the topological corrections for the string action associated with the Euler characteristic and the first Chern number of the normal bundle of the worldsheet, although do not give dynamics to the string, modify the symplectic properties of the covariant phase space of the theory. Future extensions of the present results are outlined.