Branes and DAHA Representations
Sergei Gukov · Peter Koroteev · Satoshi Nawata · Du Pei · Ingmar Saberi
2023年8月 · SpringerBriefs in Mathematical Physics 第 48 本图书 · Springer Nature
电子书
143
页
report评分和评价未经验证 了解详情
关于此电子书
In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book.
This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules.
The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction.
The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory.
This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules.
The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction.
The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory.
This is an open access book.
作者简介
Sergei Gukov is a professor of mathematics and theoretical physicist. Gukov graduated from Moscow Institute of Physics and Technology (MIPT) in Moscow, Russia before obtaining a doctorate in physics from Princeton University under the supervision of Edward Witten.[1]He held a Long-term Prize fellowship of Clay Mathematics Institute at Harvard University (2001-2006) and during 2007-2008 was a member of the school of mathematics at the Institute for Advanced Study, Princeton. Since 2007, he has been professor of mathematics and theoretical physics at the California Institute of Technology (Caltech). Starting 2010, Gukov was elected as an external scientific member of the Max Planck Society at the MPIM, Bonn.
Peter Koroteev is a lecturer at the Department of Mathematics at Univeristy of California Berkeley. He got his PhD from University of Minnesota in 2012 under supervision of Prof. Arkady Vainshtein. Since then he worked as Postdoctoral Researcher at Perimeter Institute for Theoretical Physics 2012-2016 and as Visiting Assistant Professor at University of California, Davis, 2016-2019. Peter’s work is focused on the interplay between representation theory, algebraic geometry, and mathematical physics. He is also an instructor at Berkeley and Stanford Math Circles.
Satoshi Nawata currently serves as an associate professor of physics at Fudan University. He received a Bachelor of Science at Tokyo Institute of Technology. He went on to achieve a PhD from the University of Wisconsin-Milwaukee. Following this, Satoshi Nawata had the opportunity to hold a postdoctoral position at several notable institutions, including the Tata Institute of Fundamental Research, Perimeter Institute for Theoretical Physics, NIKHEF, University of Warsaw, and the California Institute of Technology among others. He also spent time as a visiting researcher at the Max Planck Institute for Mathematics and IHES. Since 2016, Satoshi Nawata has been imparting knowledge and driving research as an Associate Professor at Fudan University./div
Du Pei is currently an associate professor of quantum mathematics at the University of Southern Denmark. He obtained his Ph.D. in theoretical physics in 2016 from Caltech, and has conducted research in theoretical physics and mathematical physics at Harvard University, MSRI, Caltech and Aarhus University. His main interests concern the geometric, algebraic and categorical properties of quantum field theory./div
Ingmar Saberi is a Senior Researcher at Ludwig-Maximilians-Universität München, Germany at Ilka Brunner's research group. Previously he was a postdoc at the University of Heidelberg, Germany in Johannes Walcher's group at the Mathematisches Institut. Ingmar got his PhD at California Institute of Technology under supervision of Prof. Sergei Gukov.
Peter Koroteev is a lecturer at the Department of Mathematics at Univeristy of California Berkeley. He got his PhD from University of Minnesota in 2012 under supervision of Prof. Arkady Vainshtein. Since then he worked as Postdoctoral Researcher at Perimeter Institute for Theoretical Physics 2012-2016 and as Visiting Assistant Professor at University of California, Davis, 2016-2019. Peter’s work is focused on the interplay between representation theory, algebraic geometry, and mathematical physics. He is also an instructor at Berkeley and Stanford Math Circles.
Satoshi Nawata currently serves as an associate professor of physics at Fudan University. He received a Bachelor of Science at Tokyo Institute of Technology. He went on to achieve a PhD from the University of Wisconsin-Milwaukee. Following this, Satoshi Nawata had the opportunity to hold a postdoctoral position at several notable institutions, including the Tata Institute of Fundamental Research, Perimeter Institute for Theoretical Physics, NIKHEF, University of Warsaw, and the California Institute of Technology among others. He also spent time as a visiting researcher at the Max Planck Institute for Mathematics and IHES. Since 2016, Satoshi Nawata has been imparting knowledge and driving research as an Associate Professor at Fudan University./div
Du Pei is currently an associate professor of quantum mathematics at the University of Southern Denmark. He obtained his Ph.D. in theoretical physics in 2016 from Caltech, and has conducted research in theoretical physics and mathematical physics at Harvard University, MSRI, Caltech and Aarhus University. His main interests concern the geometric, algebraic and categorical properties of quantum field theory./div
Ingmar Saberi is a Senior Researcher at Ludwig-Maximilians-Universität München, Germany at Ilka Brunner's research group. Previously he was a postdoc at the University of Heidelberg, Germany in Johannes Walcher's group at the Mathematisches Institut. Ingmar got his PhD at California Institute of Technology under supervision of Prof. Sergei Gukov.
为此电子书评分
欢迎向我们提供反馈意见。
如何阅读
智能手机和平板电脑
笔记本电脑和台式机
您可以使用计算机的网络浏览器聆听您在 Google Play 购买的有声读物。
电子阅读器和其他设备
如果要在 Kobo 电子阅读器等电子墨水屏设备上阅读，您需要下载一个文件，并将其传输到相应设备上。若要将文件传输到受支持的电子阅读器上，请按帮助中心内的详细说明操作。
