7,486 research outputs found
Intersection theory from duality and replica
Kontsevich's work on Airy matrix integrals has led to explicit results for
the intersection numbers of the moduli space of curves. In this article we show
that a duality between k-point functions on matrices and N-point
functions of matrices, plus the replica method, familiar in the
theory of disordered systems, allows one to recover Kontsevich's results on the
intersection numbers, and to generalize them to other models. This provides an
alternative and simple way to compute intersection numbers with one marked
point, and leads also to some new results
A note on monopole moduli spaces
We discuss the structure of the framed moduli space of Bogomolny monopoles
for arbitrary symmetry breaking and extend the definition of its stratification
to the case of arbitrary compact Lie groups. We show that each stratum is a
union of submanifolds for which we conjecture that the natural metric is
hyperKahler. The dimensions of the strata and of these submanifolds are
calculated, and it is found that for the latter, the dimension is always a
multiple of four.Comment: 17 pages, LaTe
Entanglement of superconducting charge qubits by homodyne measurement
We present a scheme by which projective homodyne measurement of a microwave
resonator can be used to generate entanglement between two superconducting
charge qubits coupled to this resonator. The non-interacting qubits are
initialised in a product of their ground states, the resonator is initialised
in a coherent field state, and the state of the system is allowed to evolve
under a rotating wave Hamiltonian. Making a homodyne measurement on the
resonator at a given time projects the qubits into an state of the form (|gg> +
exp(-i phi)|ee>)/sqrt(2). This protocol can produce states with a fidelity as
high as required, with a probability approaching 0.5. Although the system
described is one that can be used to display revival in the qubit oscillations,
we show that the entanglement procedure works at much shorter timescales.Comment: 17 pages, 7 figure
Polynomial super-gl(n) algebras
We introduce a class of finite dimensional nonlinear superalgebras providing gradings of . Odd generators close by anticommutation on polynomials (of
degree ) in the generators. Specifically, we investigate `type I'
super- algebras, having odd generators transforming in a single
irreducible representation of together with its contragredient.
Admissible structure constants are discussed in terms of available
couplings, and various special cases and candidate superalgebras are identified
and exemplified via concrete oscillator constructions. For the case of the
-dimensional defining representation, with odd generators , and even generators , , a three
parameter family of quadratic super- algebras (deformations of
) is defined. In general, additional covariant Serre-type conditions
are imposed, in order that the Jacobi identities be fulfilled. For these
quadratic super- algebras, the construction of Kac modules, and
conditions for atypicality, are briefly considered. Applications in quantum
field theory, including Hamiltonian lattice QCD and space-time supersymmetry,
are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and
reference [60
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