Strings in Background Fields

TL;DR

This paper develops an algebraic method to derive interacting quantum theories from free theories using symmetry automorphisms, applying it to string backgrounds and revealing dualities.

Contribution

It introduces a purely algebraic approach to incorporate background fields into quantum theories without classical Lagrangians, demonstrating exact solutions and dualities.

Findings

Exact algebraic solutions for theories with background fields

Discovery of periodic interactions with Kalb-Ramond background

Identification of strong-weak coupling dualities and T-duality as position-momentum duality

Abstract

In this paper free quantum theories are derived solely from their underlying symmetry group without reference to a Lagrangean or classical physics and then interactions are introduced by making use of automorphism of the symmetry algebra. It is shown how the solution of a theory interacting with background fields is obtained exactly and purely algebraically from the free theory by the action of a linear operator. The method is first applied to the harmonic oscillator interacting with a conserved current and in a second example to string theory in the presence of constant dilaton, Kalb-Ramond or gravitational fields. The derived interaction for the Kalb-Ramond background is periodic and the interactions with a dilaton respectively a gravitational field exhibit a strong-weak-coupling duality. Furthermore, it is proposed in this paper to interpret T-duality as a position-momentum duality on compact space.