Lectures on String Theory

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6. Classical fermionic superstring 92
6.1 Spinors in General Relativity 92
6.2 Superstring action and its symmetrices 99
6.3 Superconformal gauge and supermoduli 100
6.4 Action in the superconformal gauge 102
6.5 Boundary conditions 106
6.6 Superconformal algebra 107
7. Quantum fermionic string 108
7.1 Light-cone quantization and superstring spectrum 111
A. Dynamical systems of classical mechanics 119
B. OPE and conformal blocks 123
C. Useful formulae 127
D. Riemann normal coordinates 128
E. Exercises 130
1. Introduction to the course
1.1 Historical remarks
String theory arose at the end of sixties in an attempt to describe the theory of
strong interactions. In 1969 Veneziano found a beautiful formula for the scattering
amplitude of four particles. This amplitude comprised many features that physicists
expected to be found in the theory of strong interactions. It was realized very soon by
Nambu and Susskind that the underlying dynamical object from which the Veneziano
formula can be derived is a relativistic string. The fundamental difference of strings
from the theory of point particles is that strings are extended, one-dimensional,
objects; when string moves through space and time it sweeps two-dimensional surface
called the string “world-sheet”. The strings can be of two types: open – with topology
of an interval and closed – with topology of a circle.
Subsequent investigations revealed however severe difficulties to treat the string
as the theory of strong interactions. These difficulties are
1. Existence of a “critical dimension”.
2. Existence of a massless spin two particle which is absent in the hadronic world.