Topics on Strings, Branes and Calabi-Yau Compactifications

TL;DR

This paper reviews key topics in string theory, including perturbative and non-perturbative aspects, Calabi-Yau compactifications, D-branes, and dualities, highlighting their mathematical foundations and implications for four-dimensional physics.

Contribution

It provides a comprehensive overview of both perturbative and non-perturbative string theories, emphasizing recent developments in Calabi-Yau compactifications and D-brane applications.

Findings

Calabi-Yau compactifications relate to four-dimensional physics.

D-branes have diverse properties and applications.

Non-perturbative dualities like S-duality and M-theory are discussed.

Abstract

Basics of some topics on perturbative and non-perturbative string theory are reviewed. After a mathematical survey of the Standard Model of particle physics and GUTs, the bosonic string kinematics for the free case and with interaction is described. The effective action of the bosonic string and the spectrum is also discussed. Five perturbative superstring theories and their spectra is briefly outlined. Calabi-Yau three-fold compactifications of heterotic strings and their relation to some four-dimensional physics are given. T-duality in closed and open strings are surveyed. D-brane definition is provided and some of their properties and applications to brane boxes configurations, in particular to the cube model are discussed. Finally, non-perturbative issues like S-duality, M-theory, F-theory and basics of their non-perturbative Calabi-Yau compactifications are considered.