Heterotic, Open and Unoriented String Theories from Topological Membrane

TL;DR

This paper explores how topological membrane theory provides a unified three-dimensional framework for deriving various string theories, including heterotic, open, and unoriented strings, through gauge symmetries and orbifolds.

Contribution

It demonstrates the derivation of heterotic, open, and unoriented string theories from 3D topological field theories, offering new geometric interpretations and methods.

Findings

Narain constraints have a natural 3D interpretation.

Heterotic string and c=1 RCFT structure derived from 3D field theory.

Open and unoriented strings obtained via orbifolds and discrete symmetries.

Abstract

In this work are consider several topics in the Topological Membrane (TM) approach to string theory. The string dynamics is generated from the bulk physics, namely from the 3D Topologically Massive Gauge Theory (TMGT) and Topologically Massive Gravity (TMG). Both (equivalent) path integral and canonical methods of quantizing TMGT are studied. It is shown that Narain constraints on toroidal compactification (integer, even, self-dual momentum lattice) have a natural interpretation in purely three dimensional terms. The Heterotic string and the block structure of c=1 RCFT are derived from the point of view of three dimensional field theory. Open and unoriented strings in TM(GT) theory are also studied through orbifolds of the bulk 3D space. This is achieved by gauging discrete symmetries of the theory. Open and unoriented strings can be obtained from all possible realizations of C, P and T symmetries. The important role of C symmetry to distinguish between Dirichlet and Neumann boundary conditions is discussed in detail. Future directions of research in this field are also suggested and discussed.