Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry

TL;DR

This paper constructs a superconformal algebra relevant to $G_2$ string compactifications and identifies stringy mirror maps using automorphisms, linking algebraic structures with geometric mirror symmetry.

Contribution

It provides a novel realization of the Shatashvili-Vafa superconformal algebra for $G_2$ manifolds and introduces stringy mirror maps inspired by recent mathematical constructions.

Findings

Realization of superconformal algebra for $G_2$ compactifications

Identification of stringy mirror maps via automorphisms

Connection between algebraic structures and geometric mirror symmetry

Abstract

We realise the Shatashvili-Vafa superconformal algebra for $G_2$ string compactifications by combining Odake and free conformal algebras following closely the recent mathematical construction of twisted connected sum $G_2$ holonomy manifolds. By considering automorphisms of this realisation, we identify stringy analogues of two mirror maps proposed by Braun and Del Zotto for these manifolds.