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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