Simplicial and modular aspects of string dualities

TL;DR

This thesis explores the mathematical structures underlying string dualities, focusing on simplicial methods and cosmological backgrounds in superstring theories, with implications for gauge/gravity correspondence.

Contribution

It introduces new simplicial techniques for understanding string dualities and investigates superstring cosmological backgrounds, advancing theoretical insights in string theory.

Findings

Coupling between random Regge triangulations and open string theory analyzed.

Implications for gauge/gravity correspondence discussed.

Cosmological backgrounds of superstring theories explored.

Abstract

This Ph.D. thesis collects results obtained investigating two different aspects of modern unifying theories. In the first part I summarized results achieved investigating simplicial aspects of string dualities. Exploiting Boundary Conformal Field Theory techniques, I investigated the coupling between random Regge triangulations and open string theory, discussing its implications in gauge/gravity correspondence. The second part reports results obtained in the paper hep-th/0309237, devoted to look for cosmological backgrounds of superstring theories.