The course on String theory is divided into two parts,
String theory (5p) and Advanced string theory (5p). The first one
is offered in the Master program while the second, more advanced, course is
suitable for students who aim at doing a Master thesis (20p or 40p)
on a related topic.
Teachers: Docent Gabriele Ferretti and Professor Bengt E.W. Nilsson.
The course String theory begins with an introductory
discussion of the fundamental problems encountered when
trying to understand our universe in terms of standard (quantum)
field theory methods, and how
string theory may solve them. String theory is then introduced and some of
its properties studied. In particular the conformal field theory formulation,
low energy supergravity theories, scattering amplitudes,
extra dimensions and how their
compactifications are related to observed elementary particles.
D-branes and non-perturbative aspects are introduced and the
connection to eleven dimensional M-theory briefly explained.
Content: not yet decided
(will partly overlap with Chapters 1,2.1-2.2,5.1-5.3,6 of
String theory by Bengt EW Nilsson and D-branes by Gabriele Ferretti
Literature: see below and D-branes by Gabriele Ferretti
Advanced string theory is a course introducing more
advanced mathematical tools and concepts needed to penetrate deeper
into the structure of string/M theory. Loop corrections, partition
functions and Riemann surfaces are discussed, together with some recent
results connected to gauge theories, AdS/CFT, p-, D-, and M-branes, dualities
and the non-perturbative properties of
string/M theory.
Content: not yet decided (will partly overlap with
Chapters 2,4,5,8,10,11,12 of String theory by Bengt EW Nilsson
and D-branes by Gabriele Ferretti
Literature: see below and D-branes by Gabriele Ferretti
Additional literature:
1. M. Green, J. Schwarz and E. Witten, 'Superstring theory',
volume I and II
(Cambridge university press 1987).
2. J. Polchinski, 'String theory', volume I and II
(Cambridge university press 1998).
Index for the courses String theory and Advanced string theory:
Literature: lecture notes
Chapter 1
1.1 Introduction
Chapter 2: The closed uncompactified bosonic string
2.1 Operator product expansions and the Virasoro algebra
2.2 Tree amplitudes and conformal field theory
2.3 One loop amplitudes, partition functions and modular invariance
Chapter 3: The path integral formulation
3.1 Formulation of the problem
3.2 The functional measures
3.3 Tree level amplitudes, the conformal anomaly and the Liouville action
3.4 One loop amplitudes
3.5 Higher genus Riemann surfaces and the Selberg zeta-function
Chapter 4: Reparametrization ghosts
4.1 Determinants and anticommuting ghosts
4.2 The central charge and critical dimensions
4.3 Ghost number and scattering amplitudes
4.4 BRST
4.5 Bosonization of the ghost system
Chapter 5: The compactified closed bosonic string
5.1 Chiral fields and some simple self-dual lattices
5.2 Vertex operators, cocycles, and Kac-Moody algebras
5.3 Interactions in the low energy field theory
5.4 Modular invariance
5.5 The Sugawara construction
5.6 Lattices and their properties
5.7 Theta-functions and lattice partition functions
5.8 Introduction to orbifolds
Chapter 6: The fermionic string
Chapter 7: The covariant lattice approach
Chapter 8: Heterotic strings in four dimensions
Chapter 9: Reggeon formalism, g-loop vacua and the KP hierarchy
Chapter 10: Branes, Maldacena duality and black holes
Chapter 11: Low energy field theories in ten and eleven dimensions
Chapter 12: The non-perturbative structure of string/M theory
Appendix A
A1 Embedding the two sphere in three flat dimensions
A2 Stereographic projections of the two sphere
A3 CP1, Hopf fibration, the Fubini-Study metric and fiber-bundles
A4 Cohomology and Betti numbers
A5 Chern classes
A6 Tangent and line bundles
A7 Kaehler manifolds
Appendix B
B1 Basics in topology
B2 Riemann surfaces
B3 Metrics and structures on Riemann surfaces
B4 Making use of the Riemann-Roch theorem
B5 Homology and the period matrix
B6 Function theory on Riemann surfaces
Appendix C
C1 Genus one modular forms
C2 The Eisenstein series and the holomorphic anomaly
C3 Relation to doubly perioid functions
C4 Relation to quasi periodic functions
C5 Theta functions and prime forms
Appendix D
D1 Super-Riemann surfaces