A diferencial estendida para soluções aproximadas do sistema heterótico G_2

Author(s)

Hannah De Lázari da Costa e Silva

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2023-08-03

Examining board members

Henrique Nogueira de Sá Earp; Viviana Jorgelina Del Barco; Eirik Eik Svanes

• Advisor: Henrique Nogueira de Sá Earp

Abstract

In this work, we give an overview of the necessary concepts to understand recent results related to the heterotic G_2 system. We recall some facts of G_2 geometry, in particular related to the torsion of G_2-structures and to G_2 instantons. Then, we survey a class of Sasakian 7-manifolds called contact Calabi-Yau manifolds, which are realized as circle fibrations over Calabi-Yau threefolds, and admit a natural cocalibrated G_2-structure. Following this, we show some aspects of heterotic string theory, and how its 7d compactification leads to the heterotic G_2 system. We then review a recent method of calculating the infinitesimal moduli space of the heterotic G_2 system developed by de la Ossa, Larfors and Svanes (2017), and approximate solutions found by Lotay and Sá Earp (2021) on contact Calabi-Yau manifolds. Finally, we show two original results related to the properties of these approximate solutions: that the extended differential defined by these solutions don't define the cohomology necessary for de la Ossa's calculations, and that these solutions aren't compatible with the Saskian holomorphic bundle structure for the tangent space of the base manifold (AU)

• FAPESP's process: 20/15525-5 - Supersymmetric Yang-Mills theory on contact Calabi-Yau 7-manifolds
• Grantee: Hannah de Lázari da Costa e Silva
• Support Opportunities: Scholarships in Brazil - Master