
TL;DR
This paper generalizes Hamiltonians for chiral supersymmetric gauge theories at small volume, describing Cartan monopoles as lattice monopole systems with quantized parameters, for various gauge groups.
Contribution
It introduces explicit Hamiltonian constructions for Cartan monopoles in certain gauge groups, extending monopole concepts to supersymmetric gauge theories.
Findings
Explicit Hamiltonians for SU(3), SU(4), and SU(5)
Description of Cartan monopoles as lattice monopole systems
Quantization of the generalized magnetic charge
Abstract
The effective Hamiltonians for chiral supersymmetric gauge theories at small spatial volume are generalizations of the Hamiltonians describing the motion of a scalar or a spinor particle in a field of Dirac monopoles (we are dealing in fact with a certain lattice of monopoles supplemented with a periodic singular potential). The gauge fields in such Hamiltonians belong to the Cartan subalgebras of the corresponding gauge algebras. Such a construction exists for all groups admitting complex representations, i.e. for with and . We give explicit expressions for these Hamiltonians for , and for . The simplified version of such a Hamiltonian, deprived of fermion terms, of the extra scalar potential and when only one node of the lattice is taken into consideration, describe a -dimensional motion ( being…
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Quantum Chromodynamics and Particle Interactions · Particle physics theoretical and experimental studies
