# Author Archives: Carlos Shahbazi

## Metric structures in General Relativity

Reference contains the following statement:

“Ashtekar’s formulation of general relativity taught us to think of gravitational theories as theories of connections, on a bare manifold with no metric structure. […] The idea that general relativity has its deepest formulation […]

## On the spin geometry of String Theory

The purpose of this note is to introduce the reader to the notion of Lipschitz structure and its potential applications to the spin geometry required to globally formulate string theory and supergravity on a differentiable manifold.

Spinors are a crucial […]

## The geometry of String Compactifications (III): exploring the Calabi-Yau manifold

In the previous articles (I, II), we have characterized the simplest class of supersymmetric heterotic compactification backgrounds. In particular, we have finished the second article with the following result:

There is a class of admissible Heterotic internal […]

## The geometry of String Theory compactifications (II): finding the Calabi-Yau manifold

This is the second of the series of articles on the geometry of String Theory compactifications. Before reading this note, the interested reader may want to read the first note, where the concept of compactification background is introduced […]

## The geometry of String Theory compactifications (I): the basics.

This is first of a series of notes on the geometry of String Theory compactifications. The space-time in String Theory is often described by means of a mathematical object called manifold . Manifolds are very important objects from the […]