Lectures on Superstring Perturbation Theory

November 13 - November 28

Institut Henri Poincare

Eric D'Hoker (UCLA) and D.H. Phong (Columbia)

The IHP Lecture notes 34 can be found at

http://www.math.ias.edu/QFT/spring/index.html

The rigourous derivation of the two-loop superstrings amplitude can be found in:

E. D'Hoker and D.H. Phong : Two-loop superstrings

I - Main formulas (hep-th/0110247)

II - The chiral measure on moduli space (hep-th/0110283)

III - Slice independence and absence of ambiguities (hep-th/0111016)

IV - The cosmological constant and modular forms (hep-th/0111040)

Lecture 1 SPECTRUM OF FERMIONIC STRINGS

• Fermionic degrees of freedom on strings

• Quantization on a cylinder : NS and R sectors

• Local supersymmetry and invariant action on the worldsheet

• Super-Virasoro algebra and physical spectrum

Lecture 2 SPECTRUM OF SUPERSTRINGS

• GSO projection, elimination of the tachyon in NS sector

• Space-time supersymmetry of the spectrum

• Summation over spin structures

• Type IIA and Type IIB superstrings

• Heterotic strings

Lecture 3 FUNCTIONAL INTEGRAL QUANTIZATION BOSONIC STRINGS

• The space of metrics - moduli of Riemann surfaces

• Gauge fixing diffeomorphisms

• Ghost determinants, ghost fields, conformal field theory formulation

• Weyl scalings and critical dimension

• One loop amplitude

Lecture 4 TWO-DIMENSIONAL SUPERGEOMETRY

• Superfields, covariant derivatives

• Structure relations of N=1 supergeometry

• Supercomplex structures

• Supermoduli and super-period matrix

• Super Beltrami differentials

Lecture 5 FUNCTIONAL INTEGRAL QUANTIZATION SUPERSTRINGS

• Actions for matter and superghosts

• Functional Integral form of scattering amplitudes

• Superghost formulation of scattering amplitudes

• NS vertex operators

• R vertex opertors

Lecture 6 CHIRAL SPLITTING

• Chiral Splitting Theorem (scalar and ghost superfields)

• The super-prime form

• Form of the Type IIA, IIB and heterotic scattering aplitudes

• Tree level scattering amplitudes for NS-NS bosonic states

Lecture 7 SUPERSTRING ONE LOOP AMPLITUDES

• Type II one loop amplitudes for NS-NS bosons (even spin structures)

• Type II one loop amplitudes for NS-NS bosons (odd spin structures)

• Heterotic One loop amplitudes

• Unitarity, the i prescription, dispersion relations

Lecture 8 SUPERSTRING MULTILOOP AMPLITUDES

• The super period matrix and gauge fixing

• Parametrization of odd moduli slice

• Picture Changing operator and its corrections

• Amplitudes expressed in terms of theta functions