Nahm data and the mass of 1/4-BPS states

Houghton, Conor; Lee, Kimyeong

doi:10.1103/physrevd.61.106001

Cited by 7 publications

(8 citation statements)

References 27 publications

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“…A semiclassical description valid on these real co-dimension one loci -if it can be given at all -would require a discussion of moduli spaces for massless monopoles with potentials -see e.g. [136,137] -…”

Section: Jhep07(2016)071mentioning

confidence: 99%

Semiclassical framed BPS states

Moore

Royston

Bleeken

2016

J. High Energ. Phys.

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We provide a semiclassical description of framed BPS states in fourdimensional N = 2 super Yang-Mills theories probed by 't Hooft defects, in terms of a supersymmetric quantum mechanics on the moduli space of singular monopoles. Framed BPS states, like their ordinary counterparts in the theory without defects, are associated with the L 2 kernel of certain Dirac operators on moduli space, or equivalently with the L 2 cohomology of related Dolbeault operators. The Dirac/Dolbeault operators depend on two Cartan-valued Higgs vevs. We conjecture a map between these vevs and the SeibergWitten special coordinates, consistent with a one-loop analysis and checked in examples. The map incorporates all perturbative and nonperturbative corrections that are relevant for the semiclassical construction of BPS states, over a suitably defined weak coupling regime of the Coulomb branch. We use this map to translate wall crossing formulae and the no-exotics theorem to statements about the Dirac/Dolbeault operators. The no-exotics theorem, concerning the absence of nontrivial SU(2) R representations in the BPS spectrum, implies that the kernel of the Dirac operator is chiral, and further translates into a statement that all L 2 cohomology of the Dolbeault operator is concentrated in the middle degree. Wall crossing formulae lead to detailed predictions for where the Dirac operators fail to be Fredholm and how their kernels jump. We explore these predictions in nontrivial examples. This paper explains the background and arguments behind the results announced in the short note [1].

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Section: Jhep07(2016)071mentioning

confidence: 99%

Semiclassical framed BPS states

Moore

Royston

Bleeken

2016

J. High Energ. Phys.

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“…See also Ref. [180], which considers 1/4-BPS dyons in the case where the b field only breaks the SU(3) symmetry to SU(2)×U(1), with a further breaking to U(1) × U(1) arising from the second Higgs field.…”

Section: Static Forces On Monopolesmentioning

confidence: 99%

“…For this solution, however, the electric charge is fixed and incompatible with the charge quantization condition. See also Ref [180],. which considers 1/4-BPS dyons in the case where the b field only breaks the SU(3) symmetry to SU(2)×U(1), with a further breaking to U(1)×U(1) arising from the second Higgs field.…”

mentioning

confidence: 99%

Magnetic monopole dynamics, supersymmetry, and duality

2007

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We review the properties of BPS, or supersymmetric, magnetic monopoles, with an emphasis on their low-energy dynamics and their classical and quantum bound states.After an overview of magnetic monopoles, we discuss the BPS limit and its relation to supersymmetry. We then discuss the properties and construction of multimonopole solutions with a single nontrivial Higgs field. The low-energy dynamics of these monopoles is most easily understood in terms of the moduli space and its metric. We describe in detail several known examples of these. This is then extended to cases where the unbroken gauge symmetry include a non-Abelian factor.We next turn to the generic supersymmetric Yang-Mills (SYM) case, in which several adjoint Higgs fields are present. Working first at the classical level, we describe the effects of these additional scalar fields on the monopole dynamics, and then include the contribution of the fermionic zero modes to the low-energy dynamics. The resulting low-energy effective theory is itself supersymmetric. We discuss the quantization of this theory and its quantum BPS states, which are typically composed of several loosely bound compact dyonic cores.We close with a discussion of the D-brane realization of N = 4 SYM monopoles and dyons and explain the ADHMN construction of monopoles from the D-brane point of view.

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“…Finally, there are other systems for which the dynamics under influence of the potential can be analysed explicitly. While most of the SU(3) monopole systems have a very complicated metric (see Houghton and Lee [33] for details), the (1, 1) system is amenable to direct analytical analysis. Work in this direction is in progress and will be published shortly.…”

Section: Jhep12(2001)032mentioning

confidence: 99%

Motion on moduli spaces with potentials

Peeters

Zamaklar²

2001

J. High Energy Phys.

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In the limit of small velocities, the dynamics of half-BPS Yang-Mills-Higgs solitons can be described by the geodesic approximation. Recently, it has been shown that quarter-BPS states require the addition of a potential term to this approximation. We explain the logic behind this modification for a larger class of models and then analyse in detail the dynamics of two five-dimensional dyonic instantons, using both analytical and numerical techniques. Non-zero modes are shown to play a crucial role in the analysis of these systems, and we explain how these modes lead to qualitatively new types of dynamics.

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Nahm data and the mass of 1/4-BPS states

Cited by 7 publications

References 27 publications

Semiclassical framed BPS states

Semiclassical framed BPS states

Magnetic monopole dynamics, supersymmetry, and duality

Motion on moduli spaces with potentials

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