Towards a non-abelian electric-magnetic symmetry: the skeleton group

Kampmeijer, L.; Bais, F.A.; Schroers, Bernd J.; Slingerland, Joost

doi:10.1007/jhep01(2010)095

Cited by 2 publications

(1 citation statement)

References 36 publications

(97 reference statements)

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“…It is important to notice that the electric orbit is non-trivially fibered on the magnetic one. This fact is related to the difficulties to associate to non-Abelian monopoles well-defined algebraic objects, as required by quantum mechanics [21,48].…”

Section: Rational Map Construction For the Monopole Moduli Spacementioning

confidence: 99%

Non-Abelian monopoles in the Higgs phase

Nitta¹,

Vinci²

2011

Nuclear Physics B

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We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N = 2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become "non-Abelian". Kinks acquire new degrees of freedom too, and we will refer to them as "non-Abelian". As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU(N) Yang-Mills. We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the correspondence holds in the most general case. The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other wellknown techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the study of the quantum physics of non-Abelian monopoles, by considering the simpler non-Abelian kinks.

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Section: Rational Map Construction For the Monopole Moduli Spacementioning

confidence: 99%

Non-Abelian monopoles in the Higgs phase

Nitta¹,

Vinci²

2011

Nuclear Physics B

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On the Brauer Groups of Symmetries of Abelian Dijkgraaf–Witten Theories

Fuchs

Priel

Schweigert

et al. 2015

Commun. Math. Phys.

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Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group A, and with vanishing 3-cocycle, is generated by group automorphisms of A, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of A-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category A and braided auto-equivalences of its Drinfeld center Z(A). The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.

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Towards a non-abelian electric-magnetic symmetry: the skeleton group

Cited by 2 publications

References 36 publications

Non-Abelian monopoles in the Higgs phase

Non-Abelian monopoles in the Higgs phase

On the Brauer Groups of Symmetries of Abelian Dijkgraaf–Witten Theories

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