Book/Dissertation / PhD Thesis

PUBDB-2016-03141

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Quantization of super Teichmüller spaces

Aghaei, N. (Corresponding author)DESY* ; Teschner, J. (Thesis advisor)DESY*

2016
Verlag Deutsches Elektronen-Synchrotron Hamburg

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Please use a persistent id in citations: urn:nbn:de:gbv:18-79816   doi:10.3204/PUBDB-2016-03141

Report No.: DESY-THESIS-2016-021

Abstract: The quantization of the Teichmüller spaces of Riemann surfaces has found important applications to conformal field theory and N = 2 supersymmetric gauge theories. We construct a quantization of the Teichmüller spaces of super Riemann surfaces, using coordinates associated to the ideal triangulations of super Riemann surfaces.A new feature is the non-trivial dependence on the choice of a spin structure which can be encoded combinatorially in a certain refinement of the ideal triangulation. We construct a projective unitary representation of the groupoid of changes of refined ideal triangulations. Therefore, we demonstrate that the dependence of the resulting quantum theory on the choice of a triangulation is inessential. In the quantum Teichmüller theory, it was observed that the key object defining theTeichmüller theory has a close relation to the representation theory of the Borel half of Uq(sl(2)). In our research we observed that the role of Uq(sl(2)) is taken by quantum superalgebra Uq(osp(1|2)). A Borel half of Uq(osp(1|2)) is the super quantum plane. The canonical element of the Heisenberg double of the quantum super plane is evaluated in certain infinite dimensional representations on L2(R) C1|1 and compared to the flip operator from the Teichmüller theory of super Riemann surfaces.

Note: Dissertation, Universität Hamburg, 2016

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF3-611) (POF3-611)
2. GATIS - Gauge Theory as an Integrable System (317089) (317089)
3. PHGS, VH-GS-500 - PIER Helmholtz Graduate School (2015_IFV-VH-GS-500) (2015_IFV-VH-GS-500)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2016

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Database coverage:

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