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Dissertation/Thesis Abstract

Global Symmetries of Six Dimensional Superconformal Field Theories
by Merkx, Peter R., Ph.D., University of California, Santa Barbara, 2017, 552; 10620639
Abstract (Summary)

In this work we investigate the global symmetries of six-dimensional superconformal field theories (6D SCFTs) via their description in F-theory. We provide computer algebra system routines determining global symmetry maxima for all known 6D SCFTs while tracking the singularity types of the associated elliptic fibrations. We tabulate these bounds for many CFTs including every 0-link based theory. The approach we take provides explicit tracking of geometric information which has remained implicit in the classifications of 6D SCFTs to date. We derive a variety of new geometric restrictions on collections of singularity collisions in elliptically fibered Calabi-Yau varieties and collect data from local model analyses of these collisions. The resulting restrictions are sufficient to match the known gauge enhancement structure constraints for all 6D SCFTs without appeal to anomaly cancellation and enable our global symmetry computations for F-theory SCFT models to proceed similarly.

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Indexing (document details)
Advisor: Morrison, David R.
Commitee: Cooper, Daryl, Labutin, Denis
School: University of California, Santa Barbara
Department: Mathematics
School Location: United States -- California
Source: DAI-B 79/02(E), Dissertation Abstracts International
Subjects: Mathematics, Theoretical Mathematics, Theoretical physics
Keywords: Algebraic geometry, Calabi-Yau, F-theory, Gauge theory, Global symmetry, Superconformal quantum field theory
Publication Number: 10620639
ISBN: 978-0-355-42933-6
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