Lecturer **Keijo Kajantie**
(at helsinki.fi, room C224), assistant **Niko
Jokela** (at helsinki.fi, room A313)

Lectures Mon, Wed 10-12 in A315, HIP seminar room. First lecture Mon 16
Jan 2006.

Exercises Wed 12-14 in A315.

The purpose of these lectures is to go through the basics of string theory connecting, whenever possible, with recent developments. To follow them one needs first courses in mechanics, electrodynamics and quantum mechanics; general relativity would be very useful, too.

Textbook: Barton Zwiebach, A First Course in String Theory, Cambridge University Press 2004. Amazon price £35 (price comparison). This book is very detailed and often even too much so.

Supplementary reading: notes from String Theory 2005 lectured by Esko Keski-Vakkuri.

**Lecture notes:**

Pages 1 to 6: Lagrangian, action, Hamiltonian, classical relativistic particle.

Pages 7 to 12: Scalar field, electromagnetic field, gauge invariance, energy-momentum tensor, action of a classical relativistic particle moving in an electromagnetic field.

Pages 13 to 19: Path integral, classical non-relativistic string, relativistic string, Nambu-Goto action.

Pages 20 to 26: String transverse velocity, open string endpoint motion, Polyakov action (note: Zwiebach gets to this only on p. 472), symmetries of Polyakov action.

Pages 27 to 31: Symmetry currents associated with Poincare invariance, string motion in conformal gauge, Regge trajectories.

Pages 32 to 38: Three methods of quantisation, light cone gauge, mode expansions, constraints, Virasoro operators, classical dynamics with Poisson brackets.

Pages 39 to 43: Quantum string, mode creation and annihilation operators, Virasoro operators, Grassman, Lie, graded Lie, Virasoro, Kac-Moody algebras, algebra of Virasoro operators, central extension.

Pages 44 to 50: Zeta function regularisation, Casimir effect, closed string mass formula, graviton as a massless closed string state with one right and ne left moving excitation, light cone quantisation, mass formula with only physical degrees of freedom.

Pages 51 to 54: Outlining the proof of d =26, a=1, by requiring Lorentz invariance of light cone gauge quantisation.

Pages 55 to 60: Exponential density of states, string thermodynamics, maximum Hagedorn temperature.

Pages 61 to 69: Some more thermo, superstring action, superconformal gauge, periodic and antiperiodic boundary conditions, constraints from vanishing energy-momentum tensor and supercurrent.

Pages 70 to 77: Excitation spectrum of a superstring, GSO projection, superstrings in space-time, strings in background fields and Weyl invariance, supergravities, type IIA and IIB sugras. For some mysterious reason Firefox or whatever makes p. 70 landscape; this is not so in the original pdf file. Here are Pages 71 to 77 hopefully in a printable form.

Pages 78 to 80: Some stringy effects: compactification, momentum and winding modes, T-duality.