Toroidal Compactification Without Vector Structure

TL;DR

This paper explores string dualities in toroidal compactifications without vector structure, analyzing orientifold planes, their T-duality origins, and interpretations in F-theory, along with resolving a supersymmetric Yang-Mills theory puzzle.

Contribution

It provides new insights into orientifold planes and their dualities in non-vector-structured compactifications, connecting string theory, T-duality, and F-theory.

Findings

Orientifold planes with Sp(n) gauge groups arise from T-duality.

Interpretation of these planes within F-theory frameworks.

Resolution of the SO(n) supersymmetric Yang-Mills trace puzzle.

Abstract

Many important ideas about string duality that appear in conventional $\T^2$ compactification have analogs for $\T^2$ compactification without vector structure. We analyze some of these issues and show, in particular, how orientifold planes associated with $Sp(n)$ gauge groups can arise from T-duality and how they can be interpreted in F-theory. We also, in an appendix, resolve a longstanding puzzle concerning the computation of $\Tr (-1)^F$ in four-dimensional supersymmetric Yang-Mills theory with gauge group SO(n).