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Transcript

Department of Physics and Physical Oceanography Colloquium “Magnetic Monopoles: from Dirac to D-branes” Edward Olszewski Professor, Physics and Physical Oceanography UNC Wilmington The Maxwell Equations are arguably the most significant contribution to physics in the nineteenth century, unifying the theory of electricity and magnetism in a way which is not only elegant and but also esthetically pleasing. The symmetry between the electric and magnetic fields displayed within these equations is blatantly apparent. But, also apparent is the conspicuous absence of a term representing magnetic charge analogous to the electric charge. Motivated by this asymmetry Dirac modified the Maxwell Equations to include magnetic charge (magnetic monopole) and investigated the consequences. He demonstrated that the existence of a magnetic monopole necessitates not only that electric charge be quantized but also that the electric and magnetic couplings be inversely proportional to each other, i.e. so called weak/strong duality. Subsequently, 't Hooft and Polyakov showed that within the context of the spontaneously broken Yang-Mills gauge theory SO(3) magnetic monopole solutions of finite mass must necessarily exist and furthermore possess an internal structure. Consequently, Montonen and Olive conjectured that there was an exact weak/strong, electromagnetic duality for the spontaneously broken SO(3) gauge theory. More recently, this conjecture has become credible in the broader context of N=2 or N=4 Super Yang-Mills theories. Despite the lack of experimental evidence for magnetic monopoles physicists remain convinced of their existence because of compelling theoretical arguments. In our presentation we provide an overview of the Maxwell theory from a conceptual perspective and interpret the Dirac monopole within this context. We then discuss Grand Unified Theories and the 't Hooft/Polyakov monopole, emphasizing new results related to the exceptional Lie group G2. Finally, we extend the discussion to Superstring theory with primary emphasis on magnetic monopole solutions related to those discussed previously. These solutions are expecially intriguing because they expose an intimate and subtle relationship between Yang Mills Theories (Grand Unified Theories) and gravitation. Furthermore, the solutions, which constitute vacuum states in type IIb string theory, possess exotic and intriguing features, non-existent in their Yang Mills counterparts. They appear to exhibit wormhole like properties whereby the wormhole connects two D-3 branes, which can be interpreted as two different four dimensional spacetime continuums. We compare these magnetic monopole solutions to those of a magnetically charged NS5 brane, pointing out their differences. Friday, April 27, 2012 1:00 PM DeLoach Hall, Room 212 Refreshments will be served at 12:45 PM