Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory

TL;DR

This paper explores compactifications of a six-dimensional E8 theory on tori, revealing dualities, singularity structures, and their implications for string theories and Calabi-Yau spaces, offering new insights into moduli space modifications.

Contribution

It provides a novel analysis of compactifications, dualities, and singularities in string and M-theory contexts, connecting classical and quantum moduli space structures.

Findings

Derived SL(2,Z) duality of N=2, d=4, SU(2) theory with Nf=4

Provided new understanding of singularities in F-theory compactifications

Unified perspective on classical and quantum moduli space singularities

Abstract

We consider compactifications of the N=1, d=6, E_8 theory on tori to five, four, and three dimensions and learn about some properties of this theory. As a by-product we derive the SL(2,\IZ) duality of the N=2, d=4, SU(2) theory with N_f=4. Using this theory on a D-brane probe we shed new light on the singularities of F-theory compactifications to eight dimensions. As another application we consider compactifications of F-theory, M-theory and the IIA string on (singular) Calabi-Yau spaces where our theory appears in spacetime. Our viewpoint leads to a new perspective on the nature of the singularities in the moduli space and their spacetime interpretations. In particular, we have a universal understanding of how the singularities in the classical moduli space of Calabi--Yau spaces are modified by worldsheet instantons to singularities in the moduli space of the corresponding conformal field theories.