The Existence of Supersymmetric String Theory with Torsion

TL;DR

This work proves the existence of irreducible solutions to Strominger’s supersymmetric string system with torsion on a class of Calabi–Yau threefolds by perturbing around CY vacua endowed with a tangent-bundle gauge field. The authors formulate Strominger’s equations as a triplet of coupled operators $L=(L_1,L_2,L_3)$ and leverage a linearization plus an implicit-function theorem, under a nondegeneracy condition on the Kodaira–Spencer class, to extend reducible trivial solutions to irreducible ones. They provide explicit constructions on quintic and related CY threefolds by producing nontrivial deformations of the holomorphic structure on $E={\mathbb C}_X^{\oplus r}\oplus TX$ and verifying the nondegeneracy criteria, yielding SU(4) and SU(5) solutions. Together, these results establish a perturbative framework for the Strominger system with torsion and connect geometric deformations to physically relevant, regular solutions.

Abstract

We derived an existence criterion to the Supersymmetric String Theory with Torsion proposed by Strominger and proved the existence of such theory for a class of Calabi-Yau threefolds.

Theorems & Definitions (20)

• Theorem 2.1
• Lemma 2.2
• proof
• Lemma 2.3
• proof
• Lemma 3.1
• proof
• Proposition 3.2
• proof
• Proposition 3.3