The string partition function in Hull's doubled formalism

TL;DR

This paper investigates Hull's doubled formalism for string theory, demonstrating quantum equivalence to traditional models by analyzing the partition function through holomorphic factorization and the role of the topological term.

Contribution

It provides a detailed analysis of the partition function in Hull's doubled formalism, establishing its quantum equivalence to the standard string theory formulation.

Findings

Partition function derived using holomorphic factorization.

Quantum equivalence established with the standard string model.

Topological interaction term is crucial for equivalence.

Abstract

T-duality is one of the essential elements of string theory. Recently, Hull has developed a formalism where the dimension of the target space is doubled so as to make T-duality manifest. This is then supplemented with a constraint equation that allows the connection to the usual string sigma model. This paper analyses the partition function of the doubled formalism by interpreting the constraint equation as that of a chiral scalar and then using holomorphic factorisation techniques to determine the partition function. We find there is quantum equivalence to the ordinary string once the topological interaction term is included.