Mathematical Physics and String Theory

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The Quantum Siegel Algebra

Sebastian Guttenberg (Lisbon, IST)

13.12.2012 at 16:15

The Siegel Algebra is the classical gauge algebra of the Green Schwarz
superstring, generated by the Virasoro constraints and the kappa-symmetry
generator. It was presented by Siegel in 1985 and is missing a quantum
version since then. Without ghost-fields this algebra produces many operatorvalued
anomalies at quantum level. I will present strong evidence that these
anomalies can be cancelled completely within the pure spinor formalism. The
full quantum algebra turns out to be much richer and to contain some
interesting structure that was not apparent at classical level. This sheds also
new light on the role of kappa-symmetry in the pure spinor formalism, where it
was playing no role so far, while it now seems to be present in form of a
constraint. The talk is based on an on-going project with Ricardo Schiappa.
The OPE-calculations were done with a mathematica package which is
likewise still under construction.

Arnold Sommerfeld Center
Theresienstrasse 37
Room 348/349