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The BPS states of N=2 super Yang-Mills theory with gauge group SU(2) are constructed as non-trivial finite-energy solutions of the worldvolume theory of a threebrane probe in F theory. The solutions preserve 1/2 of N=2 supersymmetry and provide a worldvolume realization of strings stretching from the probe to a sevenbrane. The positions of the sevenbranes correspond to singularities in the field theory moduli space and to curvature singularities in the supergravity background. We explicitly show how the UV cut off of the effective field theory is mapped into an IR cut off in the supergravity. Finally, we discuss some features of the moduli spaces of these solutions., Comment: 26 pages, harvmac, some equations corrected in section 3. No conclusions changed, references added. Apologies to those not previously referenced, final version to appear in Nucl. Phys. B

We construct solutions of type IIB supergravity dual to N=2 super Yang-Mills theories. By considering a probe moving in a background with constant coupling and an AdS_{5} component in its geometry, we are able to reproduce the exact low energy effective action for the theory with gauge group SU(2) and N_{f}=4 massless flavors. After turning on a mass for the flavors we find corrections to the AdS_{5} geometry. In addition, the coupling shows a power law dependence on the energy scale of the theory. The origin of the power law behaviour of the coupling is traced back to instanton corrections. Instanton corrections to the four derivative terms in the low energy effective action are correctly obtained from a probe analysis. By considering a Wilson loop in this geometry we are also able to compute the instanton effects on the quark-antiquark potential. Finally we consider a solution corresponding to an asymptotically free field theory. Again, the leading form of the four derivative terms in the low energy effective action are in complete agreement with field theory expectations., Comment: 23 pages, uses harvmac, References added, typos corrected and minor improvements to discussion of N dependence, to appear in Phys. Rev. D

We show that a system of parallel D3 branes near a conifold singularity can be mapped onto an intersecting configuration of orthogonal branes in type IIA string theory. Using this brane configuration, we analyze the Higgs moduli space of the associated field theory. The dimension of the Higgs moduli space is computed from a geometrical analysis of the conifold singularity. Our results provide evidence for an extended s-rule. In addition, a discrepancy between the prediction of the brane configuration and the result obtained from a geometrical anaysis is noted. This discrepancy is traced back to worldsheet instanton effects., Comment: 23 pages, Latex, final version to appear in Nuclear Physics B

The computation of higher derivative corrections to the low energy effective actions of ${\cal N}=2$ gauge theories is considered. In particular, higher derivative corrections are computed for four dimensional ${\cal N}=2$ super Yang-Mills theory with gauge group SU(2) and $N_f=4$ hypermultiplets in the fundamental representation. The four derivative terms computed in an approach which realizes the gauge theory as the world volume theory of three branes in F theory are in agreement with the field theory result., Comment: 13 pages, uses harvmac, presentation improved, references added

In this letter we study $D$ particle quantum mechanics on a torus in the limit that one or more cycles of the torus have a zero length., Comment: 5 pages, uses harvmac

The matrix theory description of the discrete light cone quantization of $M$ theory on a $T^{2}$ is studied. In terms of its super Yang- Mills description, we identify symmetries of the equations of motion corresponding to independent rescalings of one of the world sheet light cone coordinates, which show how the $S$ duality of Type IIB string theory is realized as a Nahm-type transformation. In the $M$ theory description this corresponds to a simple $9-11$ flip., Comment: 13 pages, uses harvmac. An expanded and clarified version

In this paper the dynamics of the classical chiral $QCD_{2}$ currents is studied. We describe how the dynamics of the theory can be summarized in an equation of the Lax form, thereby demonstrating the existence of an infinite set of conserved quantities. Next, the $r$ matrix of a fundamental Poisson relation is obtained and used to demonstrate that the conserved charges Poisson commute. An underlying diffeomorphism symmetry of the equations of motion which is not a symmetry of the action is used to provide a geometric interpretation for the case of gauge group SU(2). This enables us to show that the solutions to the classical equations of motion can be identified with a large class of curves, to demonstrate an auto-B\"acklund transformation and to demonstrate a non linear superposition principle. A link between the spectral problem for $QCD_{2}$ and the solution to the closed curve problem is also demonstrated. We then go on to provide a systematic inverse scattering treatment. This formalism is used to obtain the reflectionless single boundstate eigenvalue soliton solution., Comment: 25 pages, uses harvmac

In this letter, classical chiral $QCD_{2}$ is studied in the lightcone gauge $A_{-}=0$. The once integrated equation of motion for the current is shown to be of the Lax form, which demonstrates an infinite number of conserved quantities. Specializing to gauge group SU(2), we show that solutions to the classical equations of motion can be identified with a very large class of curves. We demonstrate this correspondence explicitly for two solutions. The classical fermionic fields associated with these currents are then obtained., Comment: Final version to appear in Mod. Phys. Lett. A. A reference and two footnotes added. 6 pages revtex

In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed exactly, thereby providing an exact effective action. This effective action is shown to reproduce the familiar perturbative expansion for the two and four point functions. In particular, in the case of fermionic vector models, the effective action correctly accounts for the Fermi statistics. The theory is also studied non-perturbatively. The stationary points of the effective action are shown to provide the usual large $N$ gap equations. The homogeneous equation associated with the quadratic (in the bilocals) action is simply the two particle Bethe Salpeter equation. Finally, the leading correction in $1\over N$ is shown to be in agreement with the exact $S$ matrix of the model., Comment: 24 pages, uses REVTEX macros. Replaced with final version to appear in Phys. Rev. D

The supersymmetric collective field theory with the potential $v'(x)=\omega x-{\eta\over x}$ is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeros of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a majorana fermion. The $x$ space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed., Comment: Revtex 8 pages, Submitted to Phys. Rev. D. References and preprint numbers have been added