Generalised space-time and duality

TL;DR

This paper explores a generalized space-time framework for bosonic string theory, deriving an SO(D,D) formulation, and discusses its Hamiltonian, quantization, and symmetry properties, including implications for E11 symmetry and non-commutative field theories.

Contribution

It introduces a new SO(D,D) formulation of bosonic string theory within a generalized space-time and analyzes its Hamiltonian, quantization, and symmetry breaking mechanisms.

Findings

Derived SO(D,D) formulation of bosonic string

Presented Hamiltonian and quantization of the theory

Discussed non-commutative field theory and symmetry implications

Abstract

In this paper we consider the previously proposed generalised space-time and investigate the structure of the field theory upon which it is based. In particular, we derive a SO(D,D) formulation of the bosonic string as a non-linear realisation at lowest levels of the semi-direct product of E11 with the first fundamental representation l1. We give a Hamiltonian formulation of this theory and carry out its quantisation. We argue that the choice of representation of the quantum theory breaks the manifest SO(D,D) symmetry but that the symmetry is manifest in a non-commutative field theory. We discuss the implications for the conjectured E11 symmetry and the role of the l1 representation.