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MP: Theoretische und Mathematische Grundlagen der Physik

MP 3: Strings und Quantentheorie in externen Feldern

MP 3.1: Fachvortrag

Dienstag, 16. März 2004, 14:00–14:25, H 22

Superstrings as Dirac-Kähler systems on loop space — •Urs Schreiber — Universität Essen-Duisburg

The super Virasoro constraints of the superstring can be regarded as defining a generalized Dirac-Kähler system (d ± d^†)|ψ⟩ = 0 on the exterior bundle over loop space. Consequences and applications of this approach are discussed. In particular it is shown how various background field configurations manifest themselves as deformations of the exterior derivative on loop space, and we comment on how tensor trace divergencies due to the infinite dimensionality of loop space are related to the background equations of motion of string theory.

An interesting application of Dirac-Kähler formalism on loop space is the computation of shifts of string spectra due to perturbations of the background fields: The differential geometric formulation allows to construct a covariant Hamiltonian generator of parameter evolution along a timelike Killing vector in loop space without fixing a gauge on the worldsheet. Using this Hamiltonian one can perturbatively compute for instance curvature corrections for string excitations on AdS space close to its exactly solvable pp-wave limit.