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)

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...

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...

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.

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...

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.

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.

These notes describe how perturbative on-shell and off-shell string amplitudes can be computed using string field theory. Computational methods for approximating arbitrary amplitudes are discussed, and compared with standard world-sheet methods for computing on-shell amplitudes. These lecture notes are not self-contained; they contain the material from W. Taylor's TASI 2003 lectures not covered in the recently published ``TASI 2001'' notes {\tt hep-th/0311017} by Taylor and Z...

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.