Related papers: Canonical Nambu mechanics: relevance to string/M-t…
We give an introduction to the statistical approach to studying vacua of string/M theory, and discuss recent results of Ashok and Douglas on counting supersymmetric flux vacua in type IIb Calabi-Yau compactification. To appear in the…
We study hyper-elliptic Nambu flows associated with some $n$ dimensional maps and show that discrete integrable systems can be reproduced as flows of this class.
The physical motivations and the basic construction rules for Type I strings and M-theory compactifications are reviewed in light of the recent developments. The first part contains the basic theoretical ingredients needed for building…
We present an overview of the intimate relationship between string and D-brane dynamics, and the dynamics of gauge and gravitational fields in three spacetime dimensions. The successes, prospects and open problems in describing both…
In this short review, we outline three sets of developments in understanding heterotic string compactifications. First, we outline recent progress in heterotic analogues of quantum cohomology computations. Second, we discuss a potential…
The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms have received a lot of attention in the literature. However, a…
These lectures begin by reviewing the evidence for S duality of the toroidally compactified heterotic string in 4d that was obtained in the period 1992--94. Next they review recently discovered dualities that relate all five of the 10d…
The nature of M-theory on K3 X I, where I is a line interval, is considered, with a view towards formulating a `matrix theory' representation of that situation. Various limits of this compactification of M-theory yield a number of well…
The globalization problem arises when local tensor fields possess a given property (such as being symplectic or Poisson) but cannot be consistently extended to a global object due to incompatibilities on chart overlaps. A notable instance…
In this lecture we review some of the recent developments in string theory on an introductory and qualitative level. In particular we focus on S-T-U dualities of toroidally compactified ten-dimensional string theories and outline the…
This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…
Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that…
These lectures intend to give a pedagogical introduction into some of the developments in string theory during the last years. They include perturbative T-duality and non perturbative S- and U-dualities, their unavoidable demand for…
This is the written version of a short talk given at the University of Leipzig in December 1998. It reviews some general aspects of string theory from the viewpoint of the search for an unifying theory. Here, special emphasis lies on the…
We review the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces. This relation has made possible to give an exact solution of topological string theory on these spaces to all orders in…
The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family…
Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle,…
We investigate the connections between four-dimensional, N=2 M-theory vacua constructed as orbifolds of type II, heterotic, and type I strings. All these models have the same massless spectrum, which contains an equal number of vector…
We introduce M-theoretic generalisations of the notion of (exact) Courant algebroid, and summarise their connections to generalised geometry, U-duality, and the physics of strings, membranes, and fivebranes. This is a summary of a paper…
Wallstrom's criticism of existing formulations of stochastic mechanics is that they fail to derive the empirical predictions of orthodox quantum mechanics because they require an ad hoc quantization condition on the postulated velocity…