Families of N=2 Strings

TL;DR

This paper explores the construction of multiple N=2 string theories in 4d backgrounds by different embeddings of superconformal algebra, analyzing their parameter spaces, dualities, and D-brane spectra.

Contribution

It formulates a general principle for obtaining distinct N=2 string theories via different algebra embeddings and applies it to classify gauging choices in various 4d backgrounds.

Findings

Identifies two classes of gauging, alpha and beta, related by T-duality.

Determines parameter spaces of gauging for flat and curved 4d spaces.

Provides insights into D-brane spectra for these families.

Abstract

In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the principle of obtaining different physical theories by gauging different embeddings of the same symmetry algebra in the same ``pre-theory.'' We then apply it to N=2 strings and formulate the recipe for finding the associated parameter spaces of gauging. Flat and curved target spaces of both (4,0) and (2,2) signatures are considered. We broadly divide the gauging choices into two classes, denoted by alpha and beta, and show them to be related by T-duality. The distinction between them is formulated topologically and hinges on some unique properties of 4d manifolds. We determine what their parameter spaces of gauging are under certain simplicity ansatz for generic flat spaces (R^4 and its toroidal compactifications) as well as some curved spaces. We briefly discuss the spectra of D-branes for both alpha and beta families.