Introduction to Resurgence, Trans-series and Non-perturbative Physics III by Gerald Dunne

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
DATE:27 January 2018 to 03 February 2018
VENUE:Ramanujan Lecture Hall, ICTS Bangalore
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 problems in nonperturbative field theories interconnecting string theory, supersymmetric/superconformal field theories, quantum black holes, gravity and holography.

The content of this program can be broadly divided into five 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 supersymetry on 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.

Large N: Numerical studies based on large-N volume independence and Eguchi-Kawai (EK) reduction, meson and glueball spectra in large-N QCD, Twisted Eguchi-Kawai (TEK) reduction, numerical studies of large-N 2d QCD.

Formal Developments on the Lattice: Chiral fermions on the lattice, New approaches to solve sign problem - fermion bag approach, Lefshetz 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:

Lattice Supersymmetric Field Theories by Simon Catterall (Syracuse University, USA)
Matrix Models, Quantum Black Holes and Gravity by Masanori Hanada (Kyoto University, JAPAN)
Conformal Bootstrap by Madalena Lemos and Pedro Liendo (DESY, Hamburg, GERMANY)
Resurgence and Trans-series in Quantum Field Theories by Gerald V. Dunne (University of Connecticut, USA)

In addition to these, we plan to have single lectures on special topics of interest. During the program, Prof. David B. Kaplan (University of Washington, Seattle, USA) will be delivering the Distinguished Infosys - ICTS Chandrasekhar Lectures.

We strongly encourage students and postdocs to apply. Limited travel support is available for selected participants. There is no registration fee. Free accommodation will be provided by ICTS for non-local participants who will be selected for the program.

CONTACT US:numericalstringsbangalore@icts.res.in
PROGRAM LINK:https://www.icts.res.in/program/NUMSTRINGS2018

Table of Contents (powered by https://videoken.com)
0:01:19 Analytic Continuation of Path Integrals: Lefschetz Thimbles
0:03:31 Thimbles from Gradient Flow gradient flow to generate steepest descent thimble: A(I;
0:04:33 Complex Saddles in Path Integrals
0:07:31 Necessity of Complex Saddles
0:09:45 Resurgence, Trans-series and Non-perturbative Physics 1. Lecture 1: Basic Formalism of Trans-series and Resurgence
0:10:28 Connecting weak and strong coupling
0:10:52 "Parametric Resurgence": Both N and g?
0:13:32 Resurgence in N = 2 and N = 2" Theories (Bagar, GD, 1501.05671)
0:16:54 Resurgence of N = 2 SUSY SU(2): Mathieu Eqn Spectrum
0:18:32 Mathieu Equation Spectrum
0:19:28 Mathieu Equation Spectrum: far above the barrier
0:20:48 Beyond Large N: Multi-instantons at strong coupling
0:22:11 Resurgence in N = 2 and N = 2" Theories (fixpur, GD, 1501 85671)
0:23:11 Resurgence in N = 2 and N = 2" Theories (Ragar, GD, 1501.05671)
0:23:42 Gross-Witten-Wadia Unitary Matrix Model
0:25:29 GWW Phase Transition in 2d Gauge Theory
0:26:20 Resurgence in Matrix Models: Maridos 0806,3033, Ahmed & CD: 1710.01812 Gross-Witten-Wadia Unitary Matrix Model
0:26:40 Gross-Witten-Wadia Model: Trans-series Structure
0:28:22 Resurgence in Gross-Witten-Wadia Model
0:33:31 Resurgence in Gross-Witten-Wadia Model Ahmed & CD: 1710.01813
0:37:46 Resurgence in Gross-Witten-Wadia Model Ahmed & GD: 1710.01812
0:41:18 Resurgence in GWW: 't Hooft limit and phase transition
1:04:39 Resurgence in GWW: double-scaling limit = Painleve II
1:08:07 Conclusions

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