Generalised $G_2$-structures and type IIB superstrings

TL;DR

This paper explores how compactifying type IIB superstring theory on 6- and 7-dimensional manifolds leads to the emergence of generalized geometric structures, specifically generalized $G_2$- and SU(3)-structures, linked to string vacua.

Contribution

It establishes a connection between superstring compactifications and generalized geometries, demonstrating how specific reductions in structure groups correspond to physical string vacua.

Findings

Compactification on 7-manifolds yields generalized $G_2$-structures.

Compactification on 6-manifolds yields generalized SU(3)-structures.

These structures relate to specific reductions of the structure group in generalized geometry.

Abstract

The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group $SO(d,d)$ of the vector bundle $T^d\oplus T^{d*}$ to a special subgroup. In this article we show that compactification of IIB superstring vacua on 7-manifolds with two covariantly constant spinors leads to a generalised $G_2$-structure associated with a reduction from SO(7,7) to $G_2\times G_2$. We also consider compactifications on 6-manifolds where analogously we obtain a generalised SU(3)-structure associated with $SU(3)\times SU(3)$, and show how these relate to generalised $G_2$-structures.