Freezing of Gauge Symmetries in the Heterotic String on \(T^4\)

We derive a map relating the gauge symmetry groups of heterotic strings on \(T^4\) to other components of the moduli space with rank reduction. This generalizes the results for \(T^2\) and \(T^3\) which mirror the singularity freezing mechanism of K3 surfaces in F and M-theory, respectively. The nov...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Fraiman, Bernardo, Parra de Freitas, Héctor
Format: Article
Language:English
Subjects:
Algorithms
Freezing
M theory
Space exploration
Strings
Topology
Online Access:Get full text
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Summary:We derive a map relating the gauge symmetry groups of heterotic strings on \(T^4\) to other components of the moduli space with rank reduction. This generalizes the results for \(T^2\) and \(T^3\) which mirror the singularity freezing mechanism of K3 surfaces in F and M-theory, respectively. The novel feature in six dimensions is that the map explicitly involves the topology of the gauge groups, in particular acting only on non-simply-connected ones. This relation is equivalent to that of connected components of the moduli space of flat \(G\)-bundles over \(T^2\) with \(G\) non-simply-connected. These results are verified with a reasonably exhaustive list of gauge groups obtained with a moduli space exploration algorithm.
ISSN:2331-8422
DOI:10.48550/arxiv.2111.09966