Timelike T-duality in the string field Schrodinger functional

TL;DR

This paper explores timelike T-duality in string field theory by constructing the Schrödinger functional, revealing a symmetry that exchanges time evolution and boundary states, using Feynman diagrams and orbifold properties.

Contribution

It introduces a novel construction of the string field Schrödinger functional demonstrating timelike T-duality as a symmetry of time evolution in string theory.

Findings

Demonstrates timelike T-duality as a symmetry of string field theory.

Constructs the Schrödinger functional using Feynman diagrams.

Generalizes approach to bosonic strings on S^1/Z_2.

Abstract

Timelike T-duality of string theory appears as a symmetry of time evolution in string field theory, exchanging evolution through times t and 1/t, and exchanging boundary states with backgrounds. This is demonstrated by constructing the string field Schrodinger functional, the generator of time evolution, based on Feynman diagram arguments and in analogy with quantum field theory. There, the functional can be described using only properties of first quantised particles on a timelike orbifold. Using new sewing rules applicable to both open and closed strings we generalise this approach to bosonic string theory and express the string field Schrodinger functional in terms of strings on S^1/Z_2.