Computing Z_top

In this thesis my papers hep-th/0104190, hep-th/0310214, hep-th/0405072 and hep-th/0406065 are put into context. The thesis is mainly focused on noncommutative field theory and string theory, so results in the papers that are not related to this main theme are not discussed in detail. The thesis is almost selfcontained and in particular the first chapter might be useful as an introduction to non(anti)commutative geometry and its relation to superstring theory for beginners in...

This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of the subject. That introduction is followed by 5 chapters, where the main body of research is presented, and 4 appendices, where various standard tools and notations, which we use throughout the text, are collected.

In this work, we study a class of higher derivative couplings in the string effective action arising at the junction of topological string theory and supersymmetric gauge theories in the $\Omega$-background. They generalise a series of gravitational couplings involving gravitons and graviphotons, which reproduces the topological string theory partition function. The latter reduces, in the field theory limit, to the partition function of the gauge theory in the $\Omega$-backgr...

A polemical article evaluating string theory from the point of view of a quantum field theorist working in a mathematics department. Comments to the author are encouraged.

In this thesis we probe various interactions between toric geometry and string theory. First, the notion of a top was introduced by Candelas and Font as a useful tool to investigate string dualities. These objects torically encode the local geometry of a degeneration of an elliptic fibration. We classify all tops and give a prescription for assigning an affine, possibly twisted Kac-Moody algebra to any such top. Tops related to twisted Kac-Moody algebras can be used to constr...

This is an expositoray article on the topological string partition function promoting an extension of the partition function of open Gromov-Witten theory of CY 3-folds defined by the trace of vertex operators. We also give a brief survey of their connection to the theory of Hilbert scheme of points on surface. Specifically; we apply infinitely many Cassimir operators twisted to the vertex operator computing the amplitude. The case of finite number of twists has been well disc...

A certain topological field theory is shown to be equivalent to the compactified c=1 string. This theory is described in both Kazama-Suzuki coset and Landau-Ginzburg formulations. The genus-g partition function and genus-0 multi-tachyon correlators of the c=1 string are shown to be calculable in this approach. The KPZ formulation of non-critical string theory has a natural relation to this topological model. (Talk given at the Nato Advanced Research Workshop on `New Developme...

The aim of these notes is to give recent developments in string theory. In particular, we discuss the string spectrums, compactifications, brane physics and dualities.

These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.

Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematical Foundations of Quantum Field Theory and Perturbative String Theory".