The Monopole Equations in Topological Yang-Mills

We twist the monopole equations of Seiberg and Witten and show how these equations are realized in topological Yang-Mills theory. A Floer derivative and a Morse functional are found and are used to construct a unitary transformation between the usual Floer cohomologies and those of the monopole equations. Furthermore, these equations are seen to reside in the vanishing self-dual curvature condition of an $OSp(1|2)$-bundle. Alternatively, they may be seen arising directly from a vanishing self-dual curvature condition on an $SU(2)$-bundle in which the fermions are realized as spanning the tangent space for a specific background.Comment: 7 pgs., LaTeX (fullpage

Monopoles and the Emergence of Black Hole Entropy

One of the remarkable features of black holes is that they possess a thermodynamic description, even though they do not appear to be statistical systems. We use self-gravitating magnetic monopole solutions as tools for understanding the emergence of this description as one goes from an ordinary spacetime to one containing a black hole. We describe how causally distinct regions emerge as a monopole solution develops a horizon. We define an entropy that is naturally associated with these regions and that has a clear connection with the Hawking-Bekenstein entropy in the critical black hole limit.Comment: 6 pages, one figure RevTe

Electrolytes at spherical dielectric interfaces

A variational theory is developed and applied to study the properties of dielectric spheres immersed in a symmetric electrolyte solution. In the limit that the radius of the sphere becomes much larger than the Debye screening length, the system reduces to that of a planar dielectric interface. For this case, the excess surface tension obtained by the variational theory reduces to the Onsager-Samaras [J. Chem. Phys. 2, 528 (1934)] limiting law at low electrolyte concentrations. As the radius of the dielectric sphere decreases, the excess surface tension also decreases. The implications of this work to protein-salt interactions and the salting out of proteins are discussed

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion

Cosmological Signature of New Parity-Violating Interactions

Does Nature yield any manifestations of parity violation other than those observed in weak interactions? A map of the cosmic microwave background (CMB) temperature and polarization will provide a new signature of P violation. We give two examples of new P violating interactions, which may have something to do with Planck-scale physics, inflation, and/or quintessence, that would give rise to such a signature. Although these effects would most likely elude detection by MAP and the Planck Surveyor, they may be detectable with a future dedicated CMB polarization experiment.Comment: 4 pages, 2 figures. Origin of new terms clarified, to be published in Physical Review Letter