Motion on moduli spaces with potentials

Peeters, Kasper; Zamaklar, Marija

doi:10.1088/1126-6708/2001/12/032

Cited by 23 publications

(35 citation statements)

References 35 publications

(82 reference statements)

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“…Therefore it is natural to treat the effects of turning on Y ∞ as a perturbation, on the same footing as allowing time dependence via (4.2). This observation has also been nicely explained from the point of view of moduli space dynamics in [19,123].…”

Section: Jhep07(2016)071supporting

confidence: 62%

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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)071supporting

confidence: 62%

“…If it is violated then the monopole background is not the appropriate background to expand around. As emphasized in [19,123], it is quite natural from the point of view of the collective coordinate dynamics to tie this small parameter to the small parameter controlling the collective coordinate velocities. Thus we will assume…”

Section: Jhep07(2016)071mentioning

confidence: 99%

Semiclassical framed BPS states

Moore

Royston

Bleeken

2016

J. High Energ. Phys.

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“…This effective potential is a result of the various conserved charges in the problem, and arises in a manner similar to the effective potential found by Peeters and Zamaklar [35] in their study of a field theoretic problem related by dualities to the scattering of two supertubes.…”

Section: Jhep11(2005)026supporting

confidence: 62%

A black hole instability in five dimensions?

Marolf

Virmani

2005

J. High Energy Phys.

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Abstract:We study the moduli-space scattering of a two-charge supertube in the background of a rotating BPS D1-D5-P black hole in 4+1 dimensions, extending the static analysis of Bena and Kraus [1]. While the magnetic forces associated with this motion change the details considerably, the final conclusion is similar to that of the static analysis: we find that one can bring the supertube to the horizon, so that the BMPV black hole and the supertube merge. However, our analysis shows that this can occur even at significantly larger values of the angular momentum than was indicated by the static analysis. For a range of parameters, conservation laws and the area theorem forbid the result of the merger from being any single known object: neither near-extremal black holes nor nonsupersymmetric black rings are allowed. Such results suggest that the merger triggers an instability of the rotating D1-D5-P black hole, perhaps leading to bifurcation into a pair of black objects.

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“…Here we provide a derivation of motion of instantons along geodesics in the multi-instanton moduli space by using the adiabatic approach. Generalizing [11], we will consider this approach for instantons not only in four but also in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Scattering of instantons, monopoles and vortices in higher dimensions

Иванова¹

2016

Int. J. Geom. Methods Mod. Phys.

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We consider Yang-Mills theory on manifolds R×X with a d-dimensional Riemannian manifold X of special holonomy admitting gauge instanton equations. Instantons are considered as particlelike solutions in d + 1 dimensions whose static configurations are concentrated on X. We study how they evolve in time when considered as solutions of the Yang-Mills equations on R × X with moduli depending on time t ∈ R. It is shown that in the adiabatic limit, when the metric in the X direction is scaled down, the classical dynamics of slowly moving instantons corresponds to a geodesic motion in the moduli space M of gauge instantons on X. Similar results about geodesic motion in the moduli space of monopoles and vortices in higher dimensions are briefly discussed.

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Motion on moduli spaces with potentials

Cited by 23 publications

References 35 publications

Semiclassical framed BPS states

Semiclassical framed BPS states

A black hole instability in five dimensions?

Scattering of instantons, monopoles and vortices in higher dimensions

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