3GE Collection on Mathematics String Theory and M-Theory A Modern Introduction

String theory exists in an attempt to join the ideas of Einstein's general theory of relativity with quantum mechanics, put together to apply quantum theory to gravity. String theory inspired the whole research area of supersymmetry; string theory has made important contributions to our understanding of black hole entropy; string theory has offered impressive insights into aspects of the quark gluon plasma; string theory inspired new approaches to conventional calculations in quantum physics. In string theory, the point-like particles of particle physics are replaced by one-dimensional objects called strings. Each of these five string theories arises as a special limiting case of M-theory. This theory, like its string theory predecessors, is an example of a quantum theory of gravity. Investigations of the mathematical structure of M-theory have spawned important theoretical results in physics and mathematics.
The book focuses on holographic duality as a novel method of approaching and connecting a range of diverse subjects, including quantum gravity / black holes, QCD at extreme conditions, exotic condensed matter systems, and quantum information. This book deals with the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics. The topics include are: chapter 1 is an introduction to String Model; Chapter 2 describes about Conformal field theory; Conformal field theory in two dimensions has its roots in statistical physics and it has close connections to string theory and other two-dimensional field theories in physics. Chapter 3 is String Interaction and chapter 4 introduces about supersymmetry; chapter 5 is T-duality that covers the idea of T-duality can be extended to more complicated theories, including superstring theories. Chapter 6 details on M-theory; the description of M-theory in terms of an effective action is clearly not fundamental, so string theorists are searching for alternative formulations. One proposal for an exact nonperturbative formulation of M-theory, known as Matrix theory. It is not the whole story, however, since it is only applicable for a limited class of background geometries. Finally last chapter is Flux Compactification that means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic. A flux compactification is a particular way to deal with additional dimensions required by string theory. This book will develop the basic theoretical and mathematical ideas, including the string-theoretic origin of gravity, the theory of extra dimensions of space, the connection between strings and black holes, the "landscape" of string theory, and the holographic principle.

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