Computing Z_top

A review on topological strings and the geometry of the space of two dimensional theories. (Lectures given by C. Gomez at the Enrico Fermi Summer School, Varenna, July 1994)

This is a rendering of a review talk on the state of String Theory, given at the EPS-2003 Conference, intended for a wide audience of experimental and theoretical physicists. It emphasizes general ideas rather than technical aspects.

String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in contrary, there are indications that string theory might be linked to a fundamental principle of a quantum computational character. In addition, the nature of this principle might be capable to provide some new insight into the question of...

I worked on String Theory over a period of five years during the First String Era, the most intellectually satisfying years of my scientific life. One of the early prospectors in the String Theory Mine, I was fortunate enough to contribute to the birth of this subject, which retains after these many years, its magical hold on our imaginations and expectations.

We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalised Kontsevich matrix model in the large dimension limit. We integrate out off-diagonal degrees of freedom associated to one source eigenvalue, and find an open/closed topological string partition function, thus proving open/closed duality. We match the resulting open partition function to the genera...

These are the lecture notes for a short course in topological string theory that I gave at Uppsala University in the fall of 2004. The notes are aimed at PhD students who have studied quantum field theory and general relativity, and who have some general knowledge of ordinary string theory. The main purpose of the course is to cover the basics: after a review of the necessary mathematical tools, a thorough discussion of the construction of the A- and B-model topological strin...

In this note we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten for superstring perturbation theory in arXiv:1209.5461. We intend to make the construction geometrical in nature, by using supergeometry techniques extensively. The goal is to establish the foundation of studying topological string amplitudes in terms of integration over appropriate supermoduli spaces.

These are the lecture notes of the introductory String Theory course held by one of the authors for the master program of Theoretical Physics at Turin University. The world-sheet approach to String Theory is pedagogically introduced in the framework of the bosonic string and of the superstring.

You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free probability theory, gauge theories, to name a few. The goal of these lecture notes is certainly not to explain all these applications of the topological recursion framework. Rather, the intention is to provide a down-to-earth (and hopefully ...

I present a brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory. It is emphasized how the application of different field and string theory methods has led to important progress, opening entirely new points of view in the context of Gromov-Witten invariants, Donaldson invariants, and quantum-group invariants for knots and links.