String Theory Geometry And Mock Modular Forms PDF Download
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| Author | : Sarah Harrison |
| Publisher | : |
| Total Pages | : |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
Download String Theory, Geometry and (mock) Modular Forms Book in PDF, ePub and Kindle
Monstrous moonshine (Conway and Norton, c. 1980) is a relation between the "monster", the largest of the sporadic finite simple groups, and the j-function, the unique holomorphic weight zero modular function under SL(2, Z) with a simple pole at the infinite cusp. Recently, string theory has been the impetus for the discovery of a host of similar such relations, connecting many smaller finite groups to mock modular forms, the recalcitrant cousins of the j-function. Here I discuss some of these mysterious new connections, and progress we have made in understanding them by studying string theory on K3 manifolds. This thesis is based on the papers [157], [153], and [127] written with Miranda Cheng, Xi Dong, John Duncan, Shamit Kachru, Natalie Paquette, and Timm Wrase. It should not be cited without also referencing those papers.
| Author | : Caner Nazaroglu |
| Publisher | : |
| Total Pages | : 119 |
| Release | : 2017 |
| Genre | : |
| ISBN | : 9780355234640 |
Download Automorphic Forms and Mock Modular Forms in String Theory Book in PDF, ePub and Kindle
We study a variety of modular invariant objects in relation to string theory. First, we focus on Jacobi forms over generic rank lattices and Siegel forms that appear in N = 2, D = 4 compactifications of heterotic string with Wilson lines. Constraints from low energy spectrum and modularity are employed to deduce the relevant supersymmetric partition functions entirely. This procedure is applied on models that lead to Jacobi forms of index 3, 4, 5 as well as Jacobi forms over root lattices A2 and A3. These computations are then checked against an explicit orbifold model which can be Higgsed to the models under question. Models with a single Wilson line are then studied in detail with their relation to paramodular group Gammam as T-duality group made explicit. These results on the heterotic string side are then turned into predictions for geometric invariants using TypeII - Heterotic duality. Secondly, we study theta functions for indenite signature lattices of generic signature. Building on results in literature for signature (n-1,1) and (n-2,2) lattices, we work out the properties of generalized error functions which we call r-tuple error functions. We then use these functions to build such indenite theta functions and describe their modular completions.
| Author | : Noriko Yui, Helena Verrill, and Charles F. Doran |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 324 |
| Release | : |
| Genre | : Duality (Mathematics) |
| ISBN | : 9780821871577 |
Download Modular Forms and String Duality Book in PDF, ePub and Kindle
"This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.
| Author | : Ron Donagi, Michael R. Douglas |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 386 |
| Release | : 2014-12-02 |
| Genre | : Mathematics |
| ISBN | : 1470410516 |
Download String-Math 2013 Book in PDF, ePub and Kindle
This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.
| Author | : Philipp Fleig |
| Publisher | : Cambridge University Press |
| Total Pages | : 588 |
| Release | : 2018-07-05 |
| Genre | : Mathematics |
| ISBN | : 1108118992 |
Download Eisenstein Series and Automorphic Representations Book in PDF, ePub and Kindle
This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.
| Author | : Shing-Tung Yau |
| Publisher | : Il Saggiatore |
| Total Pages | : 398 |
| Release | : 2010-09-07 |
| Genre | : Mathematics |
| ISBN | : 0465020232 |
Download The Shape of Inner Space Book in PDF, ePub and Kindle
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
| Author | : Katrin Becker |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 120 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821836633 |
Download Snowbird Lectures on String Geometry Book in PDF, ePub and Kindle
The interaction and cross-fertilization of mathematics and physics is ubiquitous in the history of both disciplines. In particular, the recent developments of string theory have led to some relatively new areas of common interest among mathematicians and physicists, some of which are explored in the papers in this volume. These papers provide a reasonably comprehensive sampling of the potential for fruitful interaction between mathematicians and physicists that exists as a result of string theory.
| Author | : Kathrin Bringmann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 409 |
| Release | : 2017-12-15 |
| Genre | : Mathematics |
| ISBN | : 1470419440 |
Download Harmonic Maass Forms and Mock Modular Forms: Theory and Applications Book in PDF, ePub and Kindle
Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.
| Author | : Winfried Kohnen |
| Publisher | : Springer |
| Total Pages | : 370 |
| Release | : 2014-08-22 |
| Genre | : Mathematics |
| ISBN | : 3662438313 |
Download Conformal Field Theory, Automorphic Forms and Related Topics Book in PDF, ePub and Kindle
This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics. The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson. The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH).
| Author | : Yang-Hui He |
| Publisher | : Springer Nature |
| Total Pages | : 214 |
| Release | : 2021-07-31 |
| Genre | : Mathematics |
| ISBN | : 3030775623 |
Download The Calabi–Yau Landscape Book in PDF, ePub and Kindle
Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.
