Fakultät für Physik




TVI/TMP-TD4: Instantons and Black Holes – Overview

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About the lecture

Time and place

Lecture: Tue 14-16 (C112), Thu 10-12 (A249)
Tutorials: Wed 16-18 (A449)

Basic knowledge in differential geometry, gauge theory.

Contents  Plan

Solitons, Monopoles, Instantons
* Classical solutions of non-trivial topology
* Energy functional, topological sectors
* t’Hooft-Polyakov monopole, Witten effect
* Bogomolnyi bound, quantization conditions, BPS condition
* Homotopy, Holonomy
* ADHM construction
* Collective Coordinates & Moduli Spaces
* Solitons/black holes as D-branes

Non-perturbative phenomena in gauge and string theory
* Instanton effects
* Seiberg-Witten Theory

(If time, selection from
Geometric realizations in string theory
Dyons, black holes, worldsheet- and space-time-instantons
SW-Theory in string theory
Coupling to gravity

* M. Nakahara, “Geometry, Topology and Physics”
* D. Tong , “TASI lectures on solitons“, [http://arxiv.org/abs/hep-th/0509216]
* S. Coleman, "Aspects of symmetry"
* Cheng & Li, "Gauge theory of elementary particles"
* B. Felsager, "Geometry, Particles and Fields"
* Dorey & Hollowood & ... "The Calculus of Many Instantons" , [http://arxiv.org/abs/hep-th/0206063]
* J.M.Figueroa-O’Farrill, Electromagnetic duality for children, http://www.maths.ed.ac.uk/~jmf/Teaching/Lectures/EDC.pdf