Fields, Strings, Matrices and Symmetric Products

  title={Fields, Strings, Matrices and Symmetric Products},
  author={Robbert Dijkgraaf},
In these notes we review the role played by the quantum mechanics and sigma models of symmetric products in the quantization of quantum field theories, string theory and matrix theory. 
Matrix string theory on pp-waves
After a brief review on matrix string theory on flat backgrounds, we formulate matrix string models on different pp-wave backgrounds. This will be done both in the cases of constant and variable RR
Discrete Torsion and Symmetric Products
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of
The physics and mathematics of microstates in string theory: And a monstrous Farey tail
A dissertation that delves into physical and mathematical aspects of string theory. In the first part of this work, microscopic properties string theoretic black holes are investigated. The second
Symmetric products of surfaces; a unifying theme for topology and physics
This is a review paper about symmetric products of spaces $SP^n(X):= X^n/S_n$. We focus our attention on the symmetric products of 2-manifolds and make a journey through selected topics of algebraic
Phase transitions in symmetric orbifold CFTs and universality
Since many thermodynamic properties of black holes are universal, the thermodynamics of their holographic duals should be universal too. We show how this universality is exhibited in the example of
Open String on Symmetric Product
We discuss some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete light-cone quantization (DLCQ). We first derive the
Permutation Orbifolds in the large N Limit
The space of permutation orbifolds is a simple landscape of two dimensional CFTs, generalizing the well-known symmetric orbifolds. We consider constraints which a permutation orbifold with large


Strings from matrices
Matrix description of interacting theories in six-dimensions
We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or
Elliptic genera and quantum field theory
It is shown that in elliptic cohomology — as recently formulated in the mathematical literature — the supercharge of the supersymmetric nonlinear signa model plays a role similar to the role of the
The Mathematics of Fivebranes
Fivebranes are non-perturbative objects in string theory that generalize two-dimensional conformal field theory and relate such diverse subjects as moduli spaces of vector bundles on surfaces,
Notes on theories with 16 supercharges
Matrix string theory
5D Black Holes and Matrix Strings
String theory and loop space index theorems
We study index theorems for the Dirac-Ramond operator on a compact Riemannian manifold. The existence of a group action on the loop space makes possible the definition of a character valued index