Polyakov's Lectures on String Theory

These lectures were given by Professor Alexander Polyakov when he taught a graduate course on String Theory at Princeton in the fall semesters of 2013 and 2014. Vladimir Kirilin, a student in the class, reviewed the videos and provided the notes below. Grigory Tarnopolskiy, also a student in the class, took notes in 2013 and 2014. Some of the lectures follow material presented in Polakov's "Gauge Fields and Strings" (Mathematical Reports, 1987). The lectures are presented here for your enjoyment.

The files are 0.5-1.0 GB in MP4 format. If your browser is setup with proper A/V player, a lecture will start playing in a separate window immediately. If you are connecting to a low bandwidth or congested network, you might see some artifacts in the videos. If it happens too frequently, you may download the whole file on your local disk and play it offline. The first two lectures in 2013 were not recorded well and so we have substituted in two similar lectures from the fall of 2014. We apologize that the first half sentence is missing from some of these videos. We hope Tarnopolskiy's notes can resolve any questions.

Lecture Description
Lecture 1 Landau effective action for second order phase transition in the 2d Ising model. Effect of interactions, infrared limit and critical dimension.
Lecture 2 Exact solution of 2d Ising model: introduction of the disorder parameter and the emergence of free fermions.
Lecture 3 Green's functions and scaling dimensions of the Ising model via free fermions. Particles as irreducible representations of a symmetry group.
Lecture 4 Scaling dimensions of the Ising model. From scale invariance to conformal theory.
Lecture 5 Basics of Conformal Field Theory: anomalous dimensions, symmetry generators, constraints on correlation functions.
Lecture 6 Ward Identities, Operator Product Expansion. Introduction of primary operators.
Lecture 7 Constraints on Green's functions from Ward identities. OPE with stress-energy tensor.
Lecture 8 Extended Virasoro algebra. Descendant operators. Central charge.
Lecture 9 Relation between anomalous dimensions and energies. Degenerate operators. Null states.
Lecture 10 Minimal models. Null states and equations of motion in the field theory. The Ising and tricritical Ising as minimal models.
Lecture 11 Coupling CFT to gravity. The effective action and polarization operator of the graviton in the low-energy limit.
Lecture 12 Coupling fields to gravity in 2d: light-cone gauge versus conformal gauge. Non-locality of the effective action. Removal of the descendant operators by graviton.
Lecture 13 Quantization of 2d gravity. Observable quantities. Random lattice description of 2d quantum gravity.
Lecture 14 Isolating relevant topologies in the 2d random lattice description. Superfluid and frame-dependent vacuum.
Lecture 15 Polarization operator in the medium and analytic properties in the low-energy and long wavelength limit. Response to external fields.
Lecture 16 Superfluidity and superconductivity. Emergence of defects. Proper discretization.
Lecture 17 Vortices and monopoles. Properties of Dirac monopole.
Lecture 18 Defects condensation and phase transitions. Defects as an emergent degree of freedom.
Lecture 19 Wilson loop as an order parameter. Special dimension for d-dimensional defect.
Lecture 20 Wilson and quark confinement. Frame-dependent vacuum. Rindler metric. Unruh temperature.
Lecture 21 Minkowski vacuum vs. Rindler vacuum. Black hole: in-falling and static observer. Schwarzschild and dS metric in Painleve metric and creation of particles by gravitational potential.
Lecture 22 String theory. From Wilson loops to gauge-string duality. Emergence of extra dimensions.