A note on the index bundle over the moduli space of monopoles

Donaldson has shown that the moduli space of monopoles $M_k$ is diffeomorphic to the space \Rat_k of based rational maps from the two-sphere to itself. We use this diffeomorphism to give an explicit description of the bundle on \Rat_k obtained by pushing out the index bundle from $M_k$. This gives an alternative and more explicit proof of some earlier results of Cohen and Jones.Comment: 9 page

Geodesic Flow on the Normal Congruence of a Minimal Surface

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ${\Bbb{R}}^3$ and relate it to the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure

The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory

The phase structure of the finite SU(2)xSU(2) theory with N=2 supersymmetry, broken to N=1 by mass terms for the adjoint-valued chiral multiplets, is determined exactly by compactifying the theory on a circle of finite radius. The exact low-energy superpotential is constructed by identifying it as a linear combination of the Hamiltonians of a certain symplectic reduction of the spin generalized elliptic Calogero-Moser integrable system. It is shown that the theory has four confining, two Higgs and two massless Coulomb vacua which agrees with a simple analysis of the tree-level superpotential of the four-dimensional theory. In each vacuum, we calculate all the condensates of the adjoint-valued scalars.Comment: 12 pages, JHEP.cl

Gaugino condensation in an improved heterotic M-theory

Gaugino condensation is discussed in the context of a consistent new version of low energy heterotic M-theory. The four dimensional reduction of the theory is described, based on simple boson and fermion backgrounds. This is generalised to include gaugino condenstates and various background fluxes, some with non-trivial topology. It is found that condensate and quantised flux contributions to the four-dimensional superpotential contain no corrections due to the warping of the higher dimensional metric.Comment: 11 pages, 4 figures, LaTe

Toric anti-self-dual 4-manifolds via complex geometry

Using the twistor correspondence, this article gives a one-to-one correspondence between germs of toric anti-self-dual conformal classes and certain holomorphic data determined by the induced action on twistor space. Recovering the metric from the holomorphic data leads to the classical problem of prescribing the Cech coboundary of 0-cochains on an elliptic curve covered by two annuli. The classes admitting Kahler representatives are described; each such class contains a circle of Kahler metrics. This gives new local examples of scalar-flat Kahler surfaces and generalises work of Joyce who considered the case where the distribution orthogonal to the torus action is integrable.Comment: 25 pages, 2 figures, v2 corrected some misprints, v3 corrected more misprints, published version (minus one typo

Generalized Kahler manifolds and off-shell supersymmetry

We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.Comment: 21 pages; references clarified and added; theorem generalized; typos correcte

HyperK\"ahler quotients and N=4 gauge theories in D=2

We consider certain N=4 supersymmetric gauge theories in D=2 coupled to quaternionic matter multiplets in a minimal way. These theories admit as effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained as HyperK\"ahler quotients. The example of ALE manifolds is discussed. (Based on a talk given by P. Fr\'e at the F. Gursey Memorial Conference, Istanbul, June 1994).Comment: 22 pages, Latex, no figure

Hyperkahler Metrics from Periodic Monopoles

Relative moduli spaces of periodic monopoles provide novel examples of Asymptotically Locally Flat hyperkahler manifolds. By considering the interactions between well-separated periodic monopoles, we infer the asymptotic behavior of their metrics. When the monopole moduli space is four-dimensional, this construction yields interesting examples of metrics with self-dual curvature (gravitational instantons). We discuss their topology and complex geometry. An alternative construction of these gravitational instantons using moduli spaces of Hitchin equations is also described.Comment: 23 pages, latex. v2: an erroneous formula is corrected, and its derivation is given. v3 (published version): references adde

Loop space, (2,0) theory, and solitonic strings

We present an interacting action that lives in loop space, and we argue that this is a generalization of the theory for a free tensor multiplet. From this action we derive the Bogomolnyi equation corresponding to solitonic strings. Using the Hopf map, we find a correspondence between BPS strings and BPS monopoles in four-dimensional super Yang-Mills theory. This enable us to find explicit BPS saturated solitonic string solutions.Comment: 29 pages, v3: section 5 is rewritten and string solutions are found, v4: a new section on general covariance in loop spac

A new wrinkle on the enhancon

We generalize the basic enhancon solution of Johnson, Peet and Polchinski by constructing solutions without spherical symmetry. A careful consideration of boundary conditions at the enhancon surface indicates that the interior of the supergravity solution is still flat space in the general case. We provide some explicit analytic solutions where the enhancon locus is a prolate or oblate sphere.Comment: 19 pages, no figure