Browsing by Author "Vandermeulen, Thomas"

Now showing 1 - 5 of 5
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    Anomalies, extensions, and orbifolds
    Robbins, Daniel G.; Sharpe, Eric R.; Vandermeulen, Thomas (2021-10-05)
    We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is classified by cohomology and how extending the orbifold group can remove it. Working with such extensions requires an understanding of the consistent ways in which extending groups can act on the twisted states of the original symmetry, which leads us to a discrete torsionlike choice that exists in orbifolds with trivially acting subgroups. We review a general method for constructing such extensions and investigate its application to orbifolds. Through numerous explicit examples we test the conjecture that consistent extensions should be equivalent to (in general multiple copies of) orbifolds by nonanomalous subgroups.
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    Decomposition, trivially-acting symmetries, and topological operators
    Robbins, Daniel G.; Sharpe, Eric; Vandermeulen, Thomas (American Physical Society, 2023-04)
    Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry of the theory. That is, we regard such a symmetry as a mix of topological defect lines (TDLs) and topological point operators (TPOs). TDLs related by a trivially-acting symmetry can join at a TPO to form nontrivial two-way junctions. Upon gauging, the local operators at those junctions can become vacua in a disjoint union of theories. Examining the behavior of the TPOs under gauging therefore allows us to refine decomposition by tracking the trivially-acting symmetries of each universe. Mixed anomalies between the TDLs and TPOs provide discrete torsionlike phases for the partition functions of these orbifolds, modifying the resulting decomposition. This framework also readily allows for the consideration of trivially-acting noninvertible symmetries.
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    A generalization of decomposition in orbifolds
    Robbins, Daniel G.; Sharpe, Eric; Vandermeulen, Thomas (2021-10-18)
    This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds.
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    Orbifolds by 2-groups and decomposition
    Pantev, Tony; Robbins, Daniel G.; Sharpe, Eric; Vandermeulen, Thomas (2022-09-05)
    In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint union of other three-dimensional theories, which we demonstrate. These theories can be interpreted as sigma models on 2-gerbes, whose formal structures reflect properties of the orbifold construction.
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    Quantum symmetries in orbifolds and decomposition
    Robbins, Daniel G.; Sharpe, Eric; Vandermeulen, Thomas (Springer, 2022-02-14)
    In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we generalize decomposition to include orbifolds with these new phase factors, making a precise proposal for how such orbifolds are equivalent to disjoint unions of other orbifolds without trivially-acting subgroups or one-form symmetries, which we check in numerous examples.