Complex World-Sheets from N=2 Strings

TL;DR

This paper explores properties of target space strings derived from (2,1) heterotic strings, emphasizing world-sheet complexification, its target space interpretation, and implications for string field theory and spin structures.

Contribution

It introduces the concept of world-sheet complexification in (2,1) heterotic strings and relates it to non-Gaussian string field theory, supported by one-loop calculations and boundary condition analysis.

Findings

World-sheet complexification is a general property of (2,1) heterotic strings.

Finite temperature boundary conditions lead to non-chiral target space spin structures.

Problems with chiral spin structures are identified through torus partition function analysis.

Abstract

We study some properties of target space strings constructed from (2,1) heterotic strings. We argue that world-sheet complexification is a general property of the bosonic sector of such target world-sheets. We give a target space interpretation of this fact and relate it to the non-gaussian nature of free String Field Theory. We provide several one loop calculations supporting the stringy construction of critical world-sheets in terms of (2,1) models. Using finite temperature boundary conditions in the underlying (2,1) string we obtain non-chiral target space spin structures, and point out some of the problems arising for chiral spin structures, such as the heterotic world-sheet. To this end, we study the torus partition function of the corresponding asymmetric orbifold of the (2,1) string.