An Introduction to Tensor Renormalization Group by Daisuke Kadoh скачать в хорошем качестве

An Introduction to Tensor Renormalization Group by Daisuke Kadoh

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (IISER Mohali, India), Jun Nishimura (KEK Japan), David Schaich (University of Liverpool, UK) and Toby Wiseman (Imperial College London, UK) DATE: 22 August 2022 to 02 September 2022 VENUE: Ramanujan Lecture Hall, ICTS Bangalore and Online The second edition of the program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory, and Holography" aims to bring together theorists working in the areas of lattice field theory, string theory, and quantum gravity to discuss the state of the art nonperturbative methods and numerical approaches to tackle current and relevant problems in string theory and holography. The program via its strong pedagogical component aims also to build and grow a community of theorists in India who would contribute to work connecting nonperturbative field theories, string theory, supersymmetric/superconformal field theories, quantum black holes, gravity, and holography. The content of this program can be broadly divided into four topics: Lattice Supersymmetric Field Theories: Recent developments in realizing N=4 supersymmetry on the lattice (including ideas on regulating flat directions, static quark potential, anomalous dimension of Konishi operator), N=1 supersymmetry on the lattice (including fine-tuning of gluino mass, benchmark studies of confinement, gluino condensates, and gluino-glueball spectrum). Matrix Models, Quantum Black Holes and Gravity: Recent developments in matrix model holography of type II string theories/M-theory/supergravity, precision gauge-gravity duality for quantum black holes via D0 brane quantum mechanics, matrix models via large-N reductions. Conformal Bootstrap: Numerical approaches to conformal bootstrap, 2d chiral algebra-based bootstrap of protected correlators in N=2 4d SCFTs, novel approaches using 2d chiral algebra and results in anomalous dimensions in superconformal field theories, bootstrap for short (BPS) and long multiplet superconformal primaries. Formal Developments on the Lattice: New approaches to solve sign problem - fermion bag approach, Lefschetz thimbles approach and its numerical implementation, Resurgence and Trans-series in quantum mechanics and quantum field theory. We will have a series of pedagogical lectures on each of the following topics: 1. Introduction to Lattice Field Theory by Anna Hasenfratz (University of Colorado - Boulder, USA) 2. Lattice Supersymmetric Field Theories by David Schaich (University of Liverpool, UK) 3. Resurgence and Trans-series in Quantum Field Theories by Mithat Unsal (North Carolina State University, USA) 4. Bootstrap Approach to QCD by Martin Kruczenski (Purdue University, USA) 5. Holographic Cosmology by Kostas Skenderis (University of Southampton, UK) 6. Matrix Models, Gauge-Gravity Duality, and Simulations on the Lattice by Georg Bergner (University of Jena, Germany) 7. Introduction to Holography by David Berenstein (UCSB, USA) ​8. An Introduction to Tensor Renormalization Group by Daisuke Kadoh (Doshisha University, Japan) In addition to these, we will have a series of research talks on recent developments in the above-mentioned areas. CONTACT US: numstrings@icts.res.in PROGRAM LINK: https://www.icts.res.in/program/numst... Table of Contents (powered by https://videoken.com) 0:00:00 An Introduction to Tensor Renormalization Group 0:00:59 Lattice theory and Monte Carlo method 0:04:14 Cases with the sign problem 0:05:39 Tensor renormalization group (TRG) 0:07:22 Tensor diagram notation 0:09:00 Tensor networks (TNs) 0:11:10 Why is a TN? (2d Ising model) 0:15:47 Another definition of TN (2d Ising model) 0:19:31 Tensor networks in field theory 0:22:21 Talk plan 0:23:24 1. Tensor renormalization group 0:23:34 2d Ising model 0:24:00 Singular value decomposition (SVD) 0:27:37 SVD for tensors 0:30:30 Renormalization step (decomposition) 0:32:19 Tensor renormalization group 0:34:24 Numerical results in 2d Ising model 0:36:51 Renormalization step (contraction) 0:39:40 Properties of TRG 0:47:14 Discretization of scalar field 0:49:01 TN representation of scalar theory 0:51:40 Two-dimensional real phi4 theory 0:52:52 The susceptibility X = deltaphi/delta h 0:53:54 The critical coupling constant 1:00:59 The expectation value of |phi|2 1:01:10 Average phase factor 1:01:52 The expectation value of |phi|2 1:02:06 Silver Blaze vs. phase 1:04:09 Tensor renormalization group 1:06:04 2. Scalar field theory 1:08:03 Difficulty in TRG for scalars 1:08:45 Properties of TRG 1:11:17 Q&A 1:12:36 The particle number density 1:15:38 Wrap Up