Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Balachandran, A. P.; Marmo, Giuseppe; Mukunda, N.; Nilsson, Jonas; Sudarshan, E. C. G.; Zaccaria, F.

doi:10.1103/physrevd.29.2936

Cited by 23 publications

(27 citation statements)

References 9 publications

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“…One can show [46] that the action of the residual electric group maps finite energy configurations to monopole configurations with infinite energy if the magnetic charge is not invariant. The interpretation is that all BPS configurations with finite energy whose magnetic charges lie on the same electric orbit are separated by an infinite energy barrier.…”

Section: Parameter Counting For Non-abelian Monopolesmentioning

confidence: 99%

Magnetic charge lattices, moduli spaces and fusion rules

et al. 2009

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We analyze the set of magnetic charges carried by smooth BPS monopoles in Yang-MillsHiggs theory with arbitrary gauge group G spontaneously broken to a subgroup H. The charges are restricted by a generalized Dirac quantization condition and by an inequality due to Murray. Geometrically, the set of allowed charges is a solid cone in the coroot lattice of G, which we call the Murray cone. We argue that magnetic charge sectors correspond to points in the Murray cone divided by the Weyl group of H; hence magnetic charge sectors are labelled by dominant integral weights of the dual group H * . We define generators of the Murray cone modulo Weyl group, and interpret the monopoles in the associated magnetic charge sectors as basic; monopoles in sectors with decomposable charges are interpreted as composite configurations. This interpretation is supported by the dimensionality of the moduli spaces associated to the magnetic charges and by classical fusion properties for smooth monopoles in particular cases. Throughout the paper we compare our findings with corresponding results for singular monopoles recently obtained by Kapustin and Witten.

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Section: Parameter Counting For Non-abelian Monopolesmentioning

confidence: 99%

Magnetic charge lattices, moduli spaces and fusion rules

et al. 2009

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“…This is clearly attributable to the fact that the cloud size can grow without limit. 5 To avoid this difficulty, we turn to the case with a nonzero potential, where the b mode is no longer a zero mode and the MSA predicts uniform rotation of the SU(2) orientation. Because analytic results are no longer possible, we must resort to numerical solution of the field equations, both to obtain the static monopole solution, as described in the previous section, and to find the A 0 that solves the Gauss's law constraint, the topic to which we now turn.…”

Section: Constructing a Chromodyonic Configurationmentioning

confidence: 99%

“…However, Abouelsaood [1] found that, because the gauge potential has a 1/r tail in the unbroken subgroup, some of the expected zero modes are nonnormalizable, and the proposed construction does not go through. A deeper explanation for this was given by Nelson and Manohar [2], and by Balachandran et al [3][4][5], who showed that the non-Abelian Coulomb magnetic field creates a topological obstruction that prevents one from globally defining a basis for the unbroken color subgroup. This inability to define "global color" is the fundamental reason for the nonexistence of the SU(5) chromodyons 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Let us define 5) whereΦ(r, t) andÃ i (r, t) are from our numerical simulation. If the time evolution of our configuration were completely due to a slowing of the global gauge rotation, then for any given time t there would be a single θ(t) that would make ∆Φ(r, t; θ) and ∆A i (r, t; θ) both vanish for all values of r. To see how close we are to this situation, we can extract a value for θ by several different methods and then compare these values.…”

Section: Global Gauge Rotation Slow-downmentioning

confidence: 99%

“…Such objects, referred to as chromodyons, were first considered in the context of an SU(5) grand unified theory. After attempts to construct such chromodyons failed [1], it was shown that the non-Abelian magnetic charge of the SU(5) monopole creates a topological obstruction to the existence of non-Abelian "color" electric charge [2][3][4][5][6][7], and the issue was abandoned for a number of years. Since then, however, it has been realized that, with other choices of gauge group, there can be monopoles with purely Abelian magnetic charge, even though the unbroken gauge group is non-Abelian [8].…”

Section: Introductionmentioning

confidence: 99%

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Instabilities of chromodyons in SO(5) gauge theory

Guo

Weinberg

2008

Phys. Rev. D

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Attempts to construct chromodyons -objects with both magnetic charge and non-Abelian electric charge -in the context of spontaneously broken gauge theories have been thwarted in the past by topological obstructions to globally defining the unbroken non-Abelian "color" subgroup. In this paper we consider the possibility of chromodyons in a theory with SO(5) broken to SU(2) × U(1), where the topological obstructions are absent. We start by constructing a monopole with only magnetic charge. By exciting a global gauge zero mode about this monopole, we obtain a chromodyonic configuration that is an approximate solution of the field equations. We then numerically simulate the time evolution of this initial state, to see if it settles down in a stationary solution. Instead, we find that chromo-electric charge is continually radiated away, with every indication that this process will continue until this charge has been completely lost. We argue that this presents strong evidence against the existence of stable chromodyons.

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The Gauss Law: A Tale

Balachandran

Reyes-Lega

2019

Springer Proceedings in Physics

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The Gauss law plays a basic role in gauge theories, enforcing gauge invariance and creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear G/H models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with SU (3) of colour which is spontaneously broken to U (1) × U (1).Nonlinear G/H models are reformulated as gauge theories and the existence of edge states and superselection sectors in these models is also established. * We dedicate this article to our friend Alberto Ibort on the occasion of his sixtieth birthday. †

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Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Cited by 23 publications

References 9 publications

Magnetic charge lattices, moduli spaces and fusion rules

Magnetic charge lattices, moduli spaces and fusion rules

Instabilities of chromodyons in SO(5) gauge theory

The Gauss Law: A Tale

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