Nonlocal charges of T-dual strings

TL;DR

This paper investigates the properties of nonlocal conserved charges in string theory backgrounds before and after T-duality, revealing how these charges transform and differ in flat and pp-wave backgrounds.

Contribution

It provides a detailed analysis of the behavior of infinite nonlocal charges under T-duality in flat and pp-wave string backgrounds, including the introduction of conjugate variables for completeness.

Findings

Nonlocal charges are preserved under T-duality in flat backgrounds with odd-even interchange.

In pp-wave backgrounds, the independence of nonlocal charges varies between IIB and IIA cases.

A conjugate variable to the winding number is introduced to complete the charge correspondence.

Abstract

We obtain sets of infinite number of conserved nonlocal charges of strings in a flat space and pp-wave backgrounds, and compare them before and after T-duality transformation. In the flat background the set of nonlocal charges is the same before and after the T-duality transformation with interchanging odd and even-order charges. In the IIB pp-wave background an infinite number of nonlocal charges are independent, contrast to that in a flat background only the zero-th and first order charges are independent. In the IIA pp-wave background, which is the T-dualized compactified IIB pp-wave background, the zero-th order charges are included as a part of the set of nonlocal charges in the IIB background. To make this correspondence complete a variable conjugate to the winding number is introduced as a Lagrange multiplier in the IIB action a la Buscher's transformation.