String-Math 2013 : conference, June 17-21, 2013, Simons Center for Geometry and Physics, Stony Brook, NY / Ron Donagi, [and three others], editors.

Format:

Book

Conference/Event

Contributor:

Donagi, Ron, editor.

Conference Name:

String-Math (Conference) (2013 : Stony Brook, New York)

String-Math (Conference)

Series:

Proceedings of symposia in pure mathematics ; Volume 88.

Proceedings of Symposia in Pure Mathematics ; Volume 88

Language:

English

Subjects (All):

Geometry, Algebraic--Congresses.

Geometry, Algebraic.

Quantum theory--Mathematics--Congresses.

Quantum theory.

Physical Description:

1 online resource (374 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

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.

Contents:

""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Plenary talks""; ""Integrable lattice models from four-dimensional field theories""; ""1. Introduction""; ""2. Integrable lattice models""; ""3. Integrability""; ""4. Integrable models from four-dimensional field theories""; ""5. Spin-chains from =1 pure gauge theory""; ""6. Spin chains and =1 gauge theory""; ""7. Integrable systems from =2 theories""; ""References""; ""Anomalies and Invertible Field Theories""; ""1. Introduction""; ""2. Anomalies""; ""2.1. Fields and field theories: formal view""

""2.2. Anomalies: traditional view""""2.3. Anomalies: modern view""; ""3. Supersymmetric quantum mechanics""; ""3.1. Lagrangian anomaly""; ""3.2. Hamiltonian anomaly""; ""3.3. Trivializing the lagrangian and hamiltonian anomalies""; ""3.4. The anomaly as an invertible field theory""; ""4. Central simple algebras and topology""; ""4.1. Some -modules""; ""4.2. Some maps between -modules""; ""5. Supersymmetric QM with a general target""; ""References""; ""Categorical base loci and spectral gaps, via Okounkov bodies and Nevanlinna theory""; ""1. Introduction""

""2. The basic example - the category \mathinhead{A_{n}}An""""3. Experiments on \mathinhead{A_{n}}An""; ""4. Categorical base loci and categorical Okounkov bodies""; ""5. \mathinhead{K}K-calculus and Categorical Nevanlinna theory""; ""References""; ""Rankin-Selberg methods for closed string amplitudes""; ""1. Introduction""; ""2. One-loop modular integrals with trivial elliptic genus""; ""3. One-loop modular integrals with harmonic elliptic genus""; ""4. Higher-loop modular integrals""; ""References""; ""Singular Fibers and Coulomb Phases""; ""1. Introduction""

""2. Singular Elliptic Fibrations""""3. Network of small resolutions for (5)""; ""References""; ""The physics and the mixed Hodge structure of Feynman integrals""; ""\scshape Amplitudes relations and monodromies""; ""1. Unitarity methods""; ""2. Monodromy and tree-level amplitude relations""; ""2.1. Gauge theory amplitudes""; ""2.2. The gravity amplitudes""; ""\scshape Feynman integrals and periods""; ""3. Feynman integral""; ""3.1. The Feynman parametrization""; ""3.2. Ultraviolet and infrared divergences""; ""3.3. The word-line formalism""; ""4. Periods""

""5. Mixed Hodge structures for Feynman graph integrals""""5.1. Example: The massive one-loop triangle""; ""6. Variation of mixed Hodge structures""; ""6.1. Polylogarithms""; ""6.2. Polylogarithms and Feynman integrals""; ""7. Elliptic polylogarithms""; ""7.1. Mahler measure""; ""\scshape The banana integrals in two dimensions""; ""8. Schwinger representation""; ""9. The differential equation for the banana graphs at all loop orders""; ""9.1. Maple codes for the differential equations""; ""9.2. The Picard-Fuchs equation of Feynman graphs""

""10. Some explicit solutions for the all equal masses banana graphs""

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-1999-8