Physics 250 Homepage

Superstring Theory

This course is an introduction to string theory.The first part of the course will cover basic techniques for calculating the spectrumand scattering amplitudes in bosonic string theory.In the second part we will introduce supersymmetric string theories, and discuss compactification and applications to phenomenology.

Term papers:A list of suggested term papers can be foundhere.

Lectures: Ori Ganor
Email: origa@socrates.berkeley.edu
Office hours: Tuesdays 4-5pm, Thursdays 2-4pm, Birge 445

Tentative Course Plan

# Date Lecture topic Homework Solution Ref.
Introduction
1a 01/18 Introduction - - I1.1
Fundamentals of String Quantization
1b 01/20 Polyakov action - - I1
2a 01/25 Open string boundary conditions Set 1 - I1
2b 01/27 Heat Kernel Techniques - - GSW 11.4
3a 02/01 Introduction to string quantization Set 2 - I1
3b 02/03 Virasoro algebra - - I1
4a 02/08 Regge slope / closed strings - - I1
4b 02/10 Closed string spectrum / CFT - - I1-2
Conformal field theory
5a 02/15 Operator product expansion Set 3 - I2
5b 02/17 Conserved currents - - I2
- 02/21 Presidents' Day Holiday
6a 02/22 Primary fields - - I2
6b 02/24 Central charge - - I2
7a 03/01 Virasoro algebra - - I2
7b 03/03 Mode expansions - - I2
8a 03/08 State-operator correpondence Set 4 - I2
8b 03/10 Unitary CFTs - - I2
Scattering amplitudes
9a 03/15 Tree level amplitudes - - I6
9b 03/17 The Virasoro-Shapiro amplitude Set 5 - I6
- 03/21-25 Spring Recess
10a 03/29 The Polyakov path integral - - I3
10b 03/31 Moduli space and CKVs - - I5
- 04/05 Lecture Cancelled
11a 04/07 Vertex operators Set 6 - I3
11b 04/12 Classical Equations of motion - - I3
12a 04/14 One-loop Vacuum amplitudes - - I7
12b 04/19 General amplitudes - -
13a 04/21 Open-string one-loop amplitudes - - I7
The five string theories
13b 04/26 Spinors in various dimensions - - II-B
14a 04/28 Open strings - - -
14b 05/03 type-II strings - - -
15a 05/05 Heterotic strings - - -
Target space physics
15b 05/10 Low energy effective actions - - I3.7
Compactification
16a 05/12 Toroidal compactification - - II
16b 05/17 Calabi-Yau manifolds - - II


(The above course outline is subject to change.)

Hours

Book

Tools


Details of lectures

Introduction

Introduction

Planck scale; nonrenormalizability of ordinary gravity; grand unification; flat directions; moduli and their vacuum expectation values (VEVs);

A nice discussion on flat directions can be found in section 2 of Dine's lecture notes on M Theory Phenomenology [hep-th/0003175].

Fundamentals of String Quantization

Polyakov action

World-sheet; Target-space; Namb-Goto action; Polyakov action; Diffeomorphism invariance; Weyl symmetry;

Open string boundary conditions

Neumann boundary conditions; Dirichlet boundary conditions; mixed boundary conditions;

Heat Kernel Techniques

Anomalies; Weyl Anomaly; Heat Kernel; Liouville Action; critical dimension;

Introduction to string quantization

Euler number; gauge fixing; lightcone gauge; string oscillators; the tachyon;

Virasoro algebra

The longitudinal coordinate; Virasoro algebra; critical dimension; string bits; Casimir energy;

Regge slope / closed strings

Regge bound on angular momentum; Regge slope; closed strings; level-matching;

Closed string spectrum / CFT

massless spectrum; graviton; anti-symmetric 2-form; dilaton; higher dimensional free form-theories; conformal symmetry; 2-d free scalars;

Conformal field theory

Operator product expansion

Free scalar; OPEs;

Conserved currents

Ward identities and conserved currents;

Primary fields

Conformal invariance; energy-momentum tensor; conformal weights; primary fields;

Central charge

Linear dilaton CFT; bc CFT; free fermions; central charge; Schwarzian derivatve;

Virasoro algebra

Virasoro algebra; boundary conditions; the doubling trick;

Mode expansions

Mode expansions; normal ordering; ghost number anomaly;

State-operator correpondence

State-operator correspondence; SL(2,C)-invariant ground state;

Unitary CFTs

Unitary CFTs; Kac determinant; minimal models;

Scattering amplitudes

Tree level amplitudes

Tachyon and graviton vertex operators; Correlation functions on the sphere; Zamolodchikov metric;

The Virasoro-Shapiro amplitude

Calculation of the scattering amplitude for closed string tachyons;

The Polyakov path integral

Faddeev-Popov ghosts; Diff and Weyl gauge fixing; Weyl anomaly;

Moduli space and CKVs

S-matrix formula for arbitrary genus; Conformal Killing Vectors (CKVs); moduli space; Fundamental domain for a torus; Zero modes of the (b,c) ghosts and their relation to CKVs and moduli; anomaly of the bc current;

Vertex operators

The regularized Tachyon vertex operator; The graviton, dilaton and anti-symmetric tensor vertex operators;

Classical Equations of motion

One-loop Vacuum amplitudes

UV finiteness; Vacuum energy;

General amplitudes

Open-string one-loop amplitudes

Cylinder; Klein bottle; Mobious string;

The five string theories

Spinors in various dimensions

Clifford algebra; Dirac spinors; Reality condition; Weyl spinors; Majorana spinors; Majorana Weyl spinors;

Open strings

type-II strings

superconformal ghosts, periodic and anti-periodic boundary conditions,

Heterotic strings

Target space physics

Low energy effective actions

low-energy effective actions;

Compactification

Toroidal compactification

Winding number; T-duality;

Calabi-Yau manifolds

Complex manifolds; Kahler manifolds; Cohomology; Spinors;