Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
نویسندگان
چکیده
We present several results on the geometry of the quantum projective plane CPq. They include: explicit generators for the K-theory and the K-homology; a real calculus with a Hodge star operator; anti-selfdual connections on line bundles with explicit computation of the corresponding ‘monopoles’ and ‘instanton’ charges; complete diagonalization of gauged Laplacians on these line bundles; quantum invariants via equivariant K-theory and q-indices, and more.
منابع مشابه
On Optimal 4-Dimensional Metrics
We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-selfdual Riemannian metrics. The key new ingredient is a proof that the connected sum CP2#CP2#CP2#CP2#CP2 of five reverse-oriented complex projective planes admits such metrics.
متن کاملElectric and magnetic currents in SU ( 2 ) lattice gauge theory ∗
An oldest and rather popular model of the QCD vacuum is the instanton–anti-instanton media (see [1] and the references therein). It is not clear however, whether it possible to explain the confinement phenomenon within this approach [4], [2]. On the other hand, the method of abelian projections [5] is widely used in numerical calculations to study the confinement mechanism. It is clearly seen [...
متن کاملAsymptotics for Selfdual Vortices on the Torus and on the Plane: A Gluing Technique
We consider multivortex solutions for the selfdual Abelian Higgs model, as the ratio of the vortex core size to the separation distance between vortex points (the scaling parameter) tends to zero. To this end, we use a gluing technique (a shadowing lemma) for solutions to the corresponding semilinear elliptic equation on the plane, allowing any number (finite or countable) of arbitrarily prescr...
متن کاملMonopoles and Projective Representations: Two Areas of Influence of Yang–mills Theory on Mathematics
In this essay I discuss two unrelated subjects with a common theme: the influence of Yang–Mills theory on mathematics. In the first part I describe how my interest in monopole solutions in the period 1978–1980 led indirectly to the completion by Clifford Taubes of his multimonopole existence theorem during a visit to the Institute for Advanced Study in the spring of 1980. In the second part I s...
متن کاملExplicit Self - Dual Metrics On
We display explicit half-conformally-flat metrics on the connected sum of any number of copies of the complex projective plane. These metrics are obtained from magnetic monopoles in hyperbolic 3-space by an analogue of the Gibbons-Hawking ansatz, and are conformal compactifications of asymptotically-flat, scalar-flat Kahler metrics on «-fold blow-ups of C . The corresponding twistor spaces are ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009