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Register a new userOn the Kahler-Yang-Mills-Higgs equations
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Added by
Luis Alvarez-Consul
Publication date
2018
fields
Physics
and research's language is
English
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In this paper we introduce a set of equations on a principal bundle over a compact complex manifold coupling a connection on the principal bundle, a section of an associated bundle with Kahler fibre, and a Kahler structure on the base. These equations are a generalization of the Kahler-Yang-Mills equations introduced by the authors. They also generalize the constant scalar curvature for a Kahler metric studied by Donaldson and others, as well as the Yang-Mills-Higgs equations studied by Mundet i Riera. We provide a moment map interpretation of the equations, construct some first examples, and study obstructions to the existence of solutions.
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We construct the normal forms of null-Kahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism of the tangent bundle. Such metrics are examples of non-Riemannian holonomy reduction, and (in the complexified setting) appear in the Bridgeland stability conditions of the moduli spaces of Calabi-Yau three-folds. Using twistor methods we show that, in dimension four - where there is a connection with dispersionless integrability - the cohomogeneity-one anti-self-dual null-Kahler metrics are generically characterised by solutions to Painleve I or Painleve II ODEs.
We study the empirical realization of the memory effect in Yang-Mills theory with an axion-like particle, especially in view of the classical vs. quantum nature of the theory. We solve for the coupled equations of motion iteratively in the axionic contributions and explicitly display the gauge invariant effects in terms of field strengths. We apply our results in the context of heavy ion collisions, in the thin nuclear sheet limit, and point out that a probe particle traversing radiation train acquires a longitudinal null memory kick in addition to the usual transverse kick.
We study the empirical realisation of the memory effect in Yang-Mills theory, especially in view of the classical vs. quantum nature of the theory. Gauge invariant analysis of memory in classical U(1) electrodynamics and its observation by total change of transverse momentum of a charge is reviewed. Gauge fixing leads to a determination of a gauge transformation at infinity. An example of Yang-Mills memory then is obtained by reinterpreting known results on interactions of a quark and a large high energy nucleus in the theory of Color Glass Condensate. The memory signal is again a kick in transverse momentum, but it is only obtained in quantum theory after fixing the gauge, after summing over an ensemble of classical processes.
We investigate stability of pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions. We show that the pullback of a stable (resp. unstable) bundle remains stable (resp. unstable) for these classes. Assuming the graded object of a Jordan-Holder filtration to be locally free, we obtain a necessary and sufficient criterion for when the pullback of a strictly semistable vector bundle will be stable, in terms of intersection numbers on the base of the fibration. The arguments rely on adiabatic constructions of hermitian Yang-Mills connections together with the classical Donaldson-Uhlenbeck-Yau correspondence.
We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., $hat{theta} in (frac{pi}{2},frac{3pi}{2})$, on compact complex three-folds conditioned on a necessary subsolution condition. Our proof hinges on a delicate analysis of a new continuity path obtained by rewriting the equation as a generalised Monge-Amp`ere equation with mixed sign coefficients.
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