We study the behavior of D-branes at distances far shorter than the string length scale l s .We argue that short-distance phenomena are described by the IR behavior of the Dbrane world-volume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling g s this corresponds to momenta and energies far above string scale. We use 0-brane quantum mechanics to study 0-brane collisions and find structure at length scales corresponding to the eleven-dimensional Planck lengths l s ) and to the radius of the eleventh dimension in M-theory (R 11 ∼ g s l s ). We use 0-branes to probe non-trivial geometries and topologies at sub-stringy scales. We study the 0-brane 4-brane system, calculating the 0-brane moduli space metric, and find the bound state at threshold, which has characteristic size l 11 P . We examine the blowup of an orbifold and are able to resolve the resulting S 2 down to size l 11 P . A 0-brane with momentum approaching 1/R 11 is able to explore a larger configuration space in which the blowup is embedded. Analogous phenomena occur for small instantons. We finally turn to 1-branes and calculate the size of a bound state to be ∼ g
We study N = 1 supersymmetric SP (N c ) gauge theories with N f flavors of quarks in the fundamental representation. Depending on N f and N c , we find exact, dynamically generated superpotentials, smooth quantum moduli spaces of vacua, quantum moduli spaces of vacua with additional massless composites at strong coupling, confinement without chiral symmetry breaking, non-trivial fixed points of the renormalization group, and massless magnetic quarks and gluons.
4/95Supersymmetric gauge theories have the special property that certain quantities are holomorphic and can often be obtained exactly [1]. See [2] for a recent review and [3-6] for earlier work. The exact results so obtained provide insight into the dynamics of strongly coupled gauge theories, revealing a variety of interesting phenomena. It is of interest to know which phenomena are specific to particular examples and which are generic. Because the particular details appear to be very specific to the choice of gauge group and matter content, it is important to consider many different examples.
Percolation, conformai invariance, critical phenomena, conformai quantum field theory. A first version of part of the material of this paper was presented by the first author as part of the AMS Colloquium lectures in Baltimore in January 1992. The third author was supported in part by NSERC Canada and the Fonds FCAR pour l'aide et le soutien à la recherche (Québec).
We consider low energy, non-relativistic scattering of two Dirichlet zero-branes as an exercise in quantum mechanics. For weak string coupling and sufficiently small velocity, the dynamics is governed by an effective U(2) gauge theory in 0+1 dimensions. At low energies, D-brane scattering can reliably probe distances much shorter than the string scale.The only length scale in the quantum mechanics problem is the eleven dimensional Planck length. This provides evidence for the role of scales shorter than the string length in the weakly coupled dynamics of type IIA strings.
Membrane scattering in M ͑atrix͒ theory is related to dynamics in three-dimensional SU͑2͒ gauge theory, with the transfer of p 11 being an instanton process. We calculate the instanton amplitude and find precise agreement with the amplitude in eleven-dimensional supergravity. ͓S0556-2821͑97͒07020-3͔
We study N = 1 SUSY gauge theories in four dimensions with gauge group Spin (7) and N f flavors of quarks in the spinorial representation. We find that in the range 6 < N f < 15, this theory has a long distance description in terms of an SU (N f − 4) gauge theory with a symmetric tensor and N f antifundamentals. As a spin-off, we obtain by deforming along a flat direction a dual description of the theories based on the exceptional gauge group G 2 with N f fundamental flavors of quarks.6/95
We study N = 1 supersymmetric Spin(10) chiral gauge theories with a single spinor representation and N vector representations. We present a dual description in terms of an N = 1 supersymmetric SU (N − 5) chiral gauge theory with a symmetric tensor, one fundamental and N antifundamental representations. The Spin(10) theory with N = 0 breaks supersymmetry at strong coupling; we study how this arises at weak coupling in the dual theory, which is a spontaneously broken gauge theory. Also, we recover various known dualities, find new dual pairs and generate new examples of dynamical supersymmetry breaking.
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