Topological Strings And Quantum Curves PDF Download
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Author | : Lotte Hollands |
Publisher | : Amsterdam University Press |
Total Pages | : 310 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9085550203 |
Download Topological Strings and Quantum Curves Book in PDF, ePub and Kindle
This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded in string theory. Secondly, this model is generalized to a web of dualities connecting topological string theory and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann surface. This description yields a new perspective on topological string theory in terms of a KP integrable system based on a quantum curve. Thirdly, this thesis describes a geometric analysis of wall-crossing in N=4 string theory. And lastly, it offers a novel approach to constuct metastable vacua in type IIB string theory.
Author | : Ioana Coman |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : |
Download From Quantum Curves to Topological String Partition Functions Book in PDF, ePub and Kindle
Author | : Marcos Marino |
Publisher | : Oxford University Press |
Total Pages | : 210 |
Release | : 2005-09-22 |
Genre | : Science |
ISBN | : 0191524530 |
Download Chern-Simons Theory, Matrix Models, and Topological Strings Book in PDF, ePub and Kindle
In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge theory in three dimensions which describes knot and three-manifold invariants, to topological string theory, which is deeply related to Gromov-Witten invariants. This has led to some surprising relations between three-manifold geometry and enumerative geometry. This book gives the first coherent presentation of this and other related topics. After an introduction to matrix models and Chern-Simons theory, the book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implications of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory. It is written in a pedagogical style and will be useful reading for graduate students and researchers in both mathematics and physics willing to learn about these developments.
Author | : Chiu-Chu Melissa Liu |
Publisher | : American Mathematical Soc. |
Total Pages | : 549 |
Release | : 2018-11-19 |
Genre | : Topology |
ISBN | : 1470435411 |
Download Topological Recursion and its Influence in Analysis, Geometry, and Topology Book in PDF, ePub and Kindle
This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina. The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces. Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwitz numbers and Grothendieck's dessins d'enfants, Gromov-Witten invariants, the A-polynomials and colored polynomial invariants of knots, WKB analysis, and quantization of Hitchin moduli spaces. In addition to establishing these topics, the volume includes survey papers on the most recent key accomplishments: discovery of the unexpected relation to semi-simple cohomological field theories and a solution to the remodeling conjecture. It also provides a glimpse into the future research direction; for example, connections with the Airy structures, modular functors, Hurwitz-Frobenius manifolds, and ELSV-type formulas.
Author | : Vincent Bouchard: |
Publisher | : American Mathematical Soc. |
Total Pages | : 418 |
Release | : 2016-06-10 |
Genre | : Mathematics |
ISBN | : 1470419920 |
Download String-Math 2014 Book in PDF, ePub and Kindle
The conference String-Math 2014 was held from June 9–13, 2014, at the University of Alberta. This edition of String-Math is the first to include satellite workshops: “String-Math Summer School” (held from June 2–6, 2014, at the University of British Columbia), “Calabi-Yau Manifolds and their Moduli” (held from June 14–18, 2014, at the University of Alberta), and “Quantum Curves and Quantum Knot Invariants” (held from June 16–20, 2014, at the Banff International Research Station). This volume presents the proceedings of the conference and satellite workshops. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to modular forms and other arithmetic techniques. Articles in this book address many of these topics.
Author | : Amir-Kian Kashani-Poor |
Publisher | : American Mathematical Soc. |
Total Pages | : 294 |
Release | : 2018-06-06 |
Genre | : Geometry, Algebraic |
ISBN | : 1470435152 |
Download String-Math 2016 Book in PDF, ePub and Kindle
This volume contains the proceedings of the conference String-Math 2016, which was held from June 27–July 2, 2016, at Collége de France, Paris, France. String-Math is an annual conference covering the most significant progress at the interface of string theory and mathematics. The two fields have had a very fruitful dialogue over the last thirty years, with string theory contributing key ideas which have opened entirely new areas of mathematics and modern mathematics providing powerful concepts and tools to deal with the intricacies of string and quantum field theory. The papers in this volume cover topics ranging from supersymmetric quantum field theories, topological strings, and conformal nets to moduli spaces of curves, representations, instantons, and harmonic maps, with applications to spectral theory and to the geometric Langlands program.
Author | : Jose Labastida |
Publisher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2007-07-18 |
Genre | : Science |
ISBN | : 1402031777 |
Download Topological Quantum Field Theory and Four Manifolds Book in PDF, ePub and Kindle
The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.
Author | : Richard Wentworth |
Publisher | : World Scientific |
Total Pages | : 412 |
Release | : 2018-06-28 |
Genre | : Mathematics |
ISBN | : 9813229101 |
Download The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles Book in PDF, ePub and Kindle
In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.
Author | : Lotte Hollands |
Publisher | : |
Total Pages | : 124 |
Release | : 2004 |
Genre | : |
ISBN | : |
Download Counting Curves in Topological String Theory Book in PDF, ePub and Kindle
Author | : Albert S. Schwarz |
Publisher | : Springer Science & Business Media |
Total Pages | : 299 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662029987 |
Download Topology for Physicists Book in PDF, ePub and Kindle
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.