Lectures on TwoLoop Superstrings
Abstract
In these lectures, recent progress on multiloop superstring perturbation theory is reviewed. A construction from first principles is given for an unambiguous and sliceindependent twoloop superstring measure on moduli space for even spin structure. A consistent choice of moduli, invariant under local worldsheet supersymmetry is made in terms of the superperiod matrix. A variety of subtle new contributions arising from a careful gauge fixing procedure are taken into account. The superstring measure is computed explicitly in terms of genus two thetafunctions and reveals the importance of a new modular object of weight 6. For given even spin structure, the measure exhibits a behavior under degenerations of the worldsheet that is consistent with physical principles. The measure allows for a unique modular covariant GSO projection. Under this GSO projection, the cosmological constant, the 1, 2 and 3 point functions of massless supergravitons vanish pointwise on moduli space. A certain disconnected part of the 4point function is shown to be given by a convergent integral on moduli space. A general consistent formula is given for the twoloop cosmological constant in compactifications with central charge c=15 and with N=1 worldsheet supersymmetry. Finally, some comments are made on possible extensions of this work to higher loop order.
 Publication:

arXiv eprints
 Pub Date:
 November 2002
 DOI:
 10.48550/arXiv.hepth/0211111
 arXiv:
 arXiv:hepth/0211111
 Bibcode:
 2002hep.th...11111D
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Complex Variables
 EPrint:
 37 pages, 3 figures, Lectures delivered at Hangzhou and Beijing 2002