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String Theory, Geometry and (mock) Modular Forms

2014
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Release : 2014
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Book Synopsis String Theory, Geometry and (mock) Modular Forms by : Sarah Harrison

Download or read book String Theory, Geometry and (mock) Modular Forms written by Sarah Harrison. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms and Mock Modular Forms in String Theory

2017
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Release : 2017
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Book Rating : 640/5 ( reviews)

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Book Synopsis Automorphic Forms and Mock Modular Forms in String Theory by : Caner Nazaroglu

Download or read book Automorphic Forms and Mock Modular Forms in String Theory written by Caner Nazaroglu. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modular Forms and String Duality

Duality (Mathematics)
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Genre : Duality (Mathematics)
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Book Rating : 577/5 ( reviews)

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Book Synopsis Modular Forms and String Duality by : Noriko Yui, Helena Verrill, and Charles F. Doran

Download or read book Modular Forms and String Duality written by Noriko Yui, Helena Verrill, and Charles F. Doran. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: "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.

String-Math 2013

2014-12-02 Mathematics
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Release : 2014-12-02
Genre : Mathematics
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Book Rating : 516/5 ( reviews)

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Book Synopsis String-Math 2013 by : Ron Donagi, Michael R. Douglas

Download or read book String-Math 2013 written by Ron Donagi, Michael R. Douglas. This book was released on 2014-12-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Eisenstein Series and Automorphic Representations

2018-07-05 Mathematics
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Release : 2018-07-05
Genre : Mathematics
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Book Rating : 992/5 ( reviews)

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Book Synopsis Eisenstein Series and Automorphic Representations by : Philipp Fleig

Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig. This book was released on 2018-07-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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