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Speaker_	Saclioglu, Cihan
Talk_	Solutions of Seiberg-Witten and Einstein-Maxwell-Dirac equations in Euclidean signature
Abstract_	\documentclass[aps,report]{revtex4} \begin{document} \title{\Large \bf Seiberg-Witten and Einstein-Maxwell-Dirac Equations on 4-manifolds of Eucldean Signature} \author{\large Cihan Sa\c{c}l\i o\u{g}lu} \affiliation{Faculty of Engineering and Natural Sciences, Sabanci University, 34956 Tuzla, Istanbul, Turkey} %\pagestyle{empty} \maketitle The Seiberg-Witten monopole equations (SWME) \cite{sw} provide a very efficient alternative approach to Donaldson theory for the classification of smooth 4-manifolds of Euclidean signature. The three degrees of freedom involved consist of the metric, a $U(1)$ connection with self-dual field strength $F^+$ and a Weyl spinor $\psi$ that represents the monopole. The two SWME couple these fields through the Dirac equation for the spinor and by equating the tensor bilinear in the spinor to $F^+$. The underdetermined nature of the SWME is a reflection of their topological field theory origins. On the other hand, demanding that the same fields be “physical” in the sense of obeying coupled Einstein-Maxwell-Dirac equations results in an overdetermined system. Remarkably, this system admits solutions for Euclidean signature, where self-dual gauge fields and Weyl fields cannot provide non-vanishing source terms for Einstein’s or Maxwell’s field equations \cite{ac}. As a concrete example, we exhibit a class of non-singular solutions where the manifold is a product of two negative-curvature Riemann surfaces $\Sigma_{g}$ of genus $g$, there are $g$ electric vortices on one surface and $g$ magnetic ones on the other. The cosmological constant is given by a spinor condensate; the metric and the gauge field are expressed in terms of the Fuchsian function involved in the tessellation that produces Riemann surfaces from the open constant negative curvature surface \cite{cs}. \begin{thebibliography}{99} \bibitem{sw} E. Witten, Math. Res. Letters {\bf 1}, 764 (1994) \bibitem{ac} A. N. Aliev and C. Sa\c{c}l\i o\u{g}lu, Phys. Lett. B {\bf 632}, 725 (2006) \bibitem{cs} C. Sa\c{c}l\i o\u{g}lu, Class. Quantum Grav. {\bf 17},485 (2000) \end{thebibliography} \end{document}