IR Dynamics on Branes and SpaceTime Geometry.pdf

hep-th/9606017 RU-96-46 IR Dynamics on Branes and Space-Time Geometry 6 9 9 1 n Nathan Seiberg u J Department of Physics and Astronomy 0 2 Rutgers University Piscataway, NJ 08855-0849 2 v seiberg@physics.rutgers.edu 7 1 0 6 3 3 0 We consider the type I theory compactified on T . When the D5-brane wraps the T it 6 9 yields a D2-brane in seven dimensions. In the leading approximation the moduli space of / vacua of the three dimensional field theory on the brane is T 4/Z . The dual M theory h 2 t - description of this theory is a compactification on K3 and our 2-brane is the eleven dimen- p e sional 2-brane at a point in K3. We use this fact to conclude that strong coupling IR effects h : in the three dimensional theory on the brane turn its moduli space into a K3. This inter- v i X pretation allows us to solve various strongly coupled gauge theories in three dimensions by r identifying their Coulomb branch with a piece of a (sometime singular) K3. a May 1996 D-branes [1] appear to be interesting probes of space-time geometry and background gauge fields [2-6]. In particular, motivated by observations of Sen [7] the authors of [5] showed how the background τ parameter of IIB compactifications known as F theory [8] can be probed. The relevant D-brane is the D3-brane of the type II theory, whose four dimensional world volume gauge theory has such