Time Evolution in String Field Theory and T-duality

TL;DR

This paper explores how the time evolution operator in string field theory can be understood via a graphical approach, revealing a T-duality that relates different temporal evolutions and background configurations.

Contribution

It introduces a graphical derivation of the time evolution operator in second quantised string theory and demonstrates how T-duality connects different temporal and background configurations.

Findings

Graphical derivation of string theory evolution operator

T-duality relates evolution in time t to 1/t

Interchange of string fields and backgrounds under T-duality

Abstract

The time evolution operator (Schr\"odinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on the orbifold $S^1/Z_2$. We give a graphical derivation of this that generalises to second quantised string theory. T-duality then relates evolution through time t with evolution through 1/t and an interchange of string fields and backgrounds.