The Geometry of Toroidal Compactifications in String Theory PDF Download
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Author: James Alexander Gill
Publisher:
ISBN: 9780542824289
Category :
Languages : en
Pages : 252
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Book Description
Compactifications are the standard way of connecting string theory with phenomenology. Toroidal compactifications, in particular, are simple enough to be approachable, but still yield interesting dynamics in lower dimensions. We explore different aspects of toroidal compactifications, and use different tools to analyze the compactified theories. First we consider a two-dimensional torus with twisted boundary conditions for the fields. We analyze this with matrix models using the Dijkgraaf-Vafa method. Next, we move to higher dimensional compactifications. By considering M-theory on a T 10, we may use algebraic tools from the correspondence with E10. We prove that these give us a, simple way to check if two configurations (each containing two objects) are U-dual or not. Next, we use these same tools to analyze M-theory compactified on a double orbifold. We find another infinite-dimensional Lie algebra which corresponds to this theory, whose roots give information about the objects inhabiting this theory, much as the E10 correspondence does for M-theory on T10.
Author: James Alexander Gill
Publisher:
ISBN: 9780542824289
Category :
Languages : en
Pages : 252
Get Book Here
Book Description
Compactifications are the standard way of connecting string theory with phenomenology. Toroidal compactifications, in particular, are simple enough to be approachable, but still yield interesting dynamics in lower dimensions. We explore different aspects of toroidal compactifications, and use different tools to analyze the compactified theories. First we consider a two-dimensional torus with twisted boundary conditions for the fields. We analyze this with matrix models using the Dijkgraaf-Vafa method. Next, we move to higher dimensional compactifications. By considering M-theory on a T 10, we may use algebraic tools from the correspondence with E10. We prove that these give us a, simple way to check if two configurations (each containing two objects) are U-dual or not. Next, we use these same tools to analyze M-theory compactified on a double orbifold. We find another infinite-dimensional Lie algebra which corresponds to this theory, whose roots give information about the objects inhabiting this theory, much as the E10 correspondence does for M-theory on T10.
Author: Mariana Graña
Publisher: Springer
ISBN: 3319543164
Category : Science
Languages : en
Pages : 82
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Book Description
The lectures in this book provide graduate students and non-specialist researchers with a concise introduction to the concepts and formalism required to reduce the ten-dimensional string theories to the observable four-dimensional space-time - a procedure called string compactification. The text starts with a very brief introduction to string theory, first working out its massless spectrum and showing how the condition on the number of dimensions arises. It then dwells on the different possible internal manifolds, from the simplest to the most relevant phenomenologically, thereby showing that the most elegant description is through an extension of ordinary Riemannian geometry termed generalized geometry, which was first introduced by Hitchin. Last but not least, the authors review open problems in string phenomenology, such as the embedding of the Standard Model and obtaining de Sitter solutions.
Author: Alessandro Tomasiello
Publisher: Cambridge University Press
ISBN: 1108473733
Category : Science
Languages : en
Pages : 677
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Book Description
A unified perspective on new and advanced mathematical techniques used in string theory research for graduate students and researchers.
Author: Clay Mathematics Institute. Summer School
Publisher: American Mathematical Soc.
ISBN: 9780821837153
Category : Mathematics
Languages : en
Pages : 396
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Book Description
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
Author: Alessandro Tomasiello
Publisher: Cambridge University Press
ISBN: 1108614582
Category : Science
Languages : en
Pages : 678
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Book Description
String theory is a leading candidate for the unification of universal forces and matter, and one of its most striking predictions is the existence of small additional dimensions that have escaped detection so far. This book focuses on the geometry of these dimensions, beginning with the basics of the theory, the mathematical properties of spinors, and differential geometry. It further explores advanced techniques at the core of current research, such as G-structures and generalized complex geometry. Many significant classes of solutions to the theory's equations are studied in detail, from special holonomy and Sasaki–Einstein manifolds to their more recent generalizations involving fluxes for form fields. Various explicit examples are discussed, of interest to graduates and researchers.
Author: Katrin Becker
Publisher: Cambridge University Press
ISBN: 9780521860697
Category : Science
Languages : en
Pages : 756
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Book Description
String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697.
Author: Luis E. Ibáñez
Publisher: Cambridge University Press
ISBN: 0521517524
Category : Science
Languages : en
Pages : 689
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Book Description
A systematic introduction to string phenomenology, outlining how string theory is connected to the real world of particle physics.
Author: Shing-Tung Yau
Publisher: Il Saggiatore
ISBN: 0465020232
Category : Mathematics
Languages : en
Pages : 398
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Book Description
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Author: Sergio Cecotti
Publisher: Springer Nature
ISBN: 3031365305
Category : Science
Languages : en
Pages : 846
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Book Description
Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
Author: A.N. Schellekens
Publisher: Elsevier
ISBN: 0444596070
Category : Science
Languages : en
Pages : 525
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Book Description
The book includes a selection of papers on the construction of superstring theories, mainly written during the years 1984-1987. It covers ten-dimensional supersymmetric and non-supersymmetric strings, four-dimensional heterotic strings and four-dimensional type-II strings. An introduction to more recent developments in conformal field theory in relation to string construction is provided.
