Computing Z_top

This thesis is based on some selected topics in open topological string theory which I have worked on during my Ph.D. It comprises an introductory part where I have focused on the points most needed for the later chapters, trading completeness for conciseness and clarity. Then, following [12], we discuss tadpole cancellation for topological strings where we mainly show how its implementation is needed for ensuring the same "odd" moduli decoupling encountered in the closed the...

Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition function of the topological string theory from fluctuations around a classical solution in the topological string geometry theory.

This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects of these developments. First, we discuss the computational progress in the topological string partition functions on a class of elliptic Calabi-Yau manifolds. We propose to use Jacobi forms as an ansatz for the partition function. For non-co...

The purpose of this note is to provide a short invitation to the universal algebraic approach to topological string theory. In the first section we make an attempt to explain the origin of this approach and how it fits into the bigger picture of full string theory, while in the second half of this note we will introduce the relevant notions in more detail and discuss some of our main results on bulk-deformed open topological string amplitudes.

These lecture notes review the topological string theory and its applications to mathematics and physics. They expand on material presented at the Takagi Lectures of the Mathematical Society of Japan on 21 June 2008 at Department of Mathematics, Kyoto University.

At the present time, string theory (and its generalizations) remain relatively abstruse subjects to the particle phenomenologist and experimentalist. Yet, striking developments of the last two years offer hope that a fundamental non-perturbative formulation of this theory will be found, and that this formulation will permit us to make contact with supersymmetric standard-model physics. This article is based on a talk which attempted to convey the essence of these recent devel...

Unabridged version of the Thesis presented to the University of L' Aquila, in partial fulfillment of the requirements for the ``Laurea'' degree in Physics, October 1998. Work carried out at the University of L'Aquila and at the University of Rome ``Tor Vergata''.

In this thesis, we study the properties of String theory amplitudes within the framework of Intersection Theory (IT) for twisted (co)homology, which, as recently proposed, offered a novel approach to analyze relations between scattering amplitudes, in string theory as well as in QFT. As only recently pointed out, thanks to IT, the analytic properties of scattering amplitudes can be related to the topological properties of the manifolds characterizing their integral representa...

This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded into string theory. Secondly, this model is generalized to a web of dualities connecting topological string theory and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann surface. This description yi...

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.