New examples of N =2 supersymmetric conformal field theories are found as fixed points of SU (2) N =2 supersymmetric QCD. Relations among the scaling dimensions of their relevant chiral operators, global symmetries, and Higgs branches are understood in terms of the general structure of relevant deformations of non-trivial N =2 conformal field theories. The spectrum of scaling dimensions found are all those compatible with relevant deformations of a y 2 = x 3 singular curve.

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We formulate an extension of Maldacena's AdS/CFT conjectures to the case of branes located at singular points in the ambient transverse space. For singularities which occur at finite distance in the moduli space of M or F theory models with spacetimefilling branes, the conjectures identify the worldvolume theory on the p-branes with a compactification of M or IIB theory on AdS p+2 × H D−p−2 . We show how the singularity determines the horizon H, and demonstrate the relationship between global symmetries on the worldvolume and gauge symmetries in the AdS model. As a first application, we study some singularities relevant to the D3-branes required in four-dimensional F -theory.For these we are able to explicitly derive the low-energy field theory on the worldvolume and compare its properties to predictions from the dual AdS model. In particular, we examine the baryon spectra of the models and the fate of the Abelian factors in the gauge group.Spacetime-filling branes have emerged as an essential feature of string and M-theory compactifications in at least three contexts: (1) new branches of the heterotic string in six dimensions with "extra" tensor multiplets, which can be represented by a Hořava-Witten-type compactification of M-theory on (S 1 /Z 2 ) × K3 but with extra spacetimefilling M5-branes representing the extra tensor multiplets [1,2,3]; (2) F -theory models in four dimensions (which can be regarded as compactifications of the IIB string with D7branes included) which in general require spacetime-filling D3-branes to cancel a tadpole anomaly [4]; and (3) M-theory models in three dimensions, which require spacetime-filling M2-branes to cancel a similar tadpole anomaly [4]. In each of these cases, the spacetimefilling brane meets the compactifying space at a single point, and the string or M-theory remains finite near the brane. 1Remarkably, this short list of branes (M5, D3, and M2) is precisely the list of branes for which a certain scaling limit is expected to lead to a "boundary" conformal field theory in the recent AdS/CF T conjectures [5,6,7]. In fact, the scaling limit can be taken even when the space transverse to the branes is curved, as in the compactification scenarios above. The details of the metric far from the location y 0 of the brane in the transverse space become irrelevant; for the purposes of studying the scaling limit, the metric on the compactifying space can be approximated by some metric on its tangent space T y 0 at y 0 . In the scaling limit, the rescaled supergravity metric approaches a metric of the form AdS p+2 × S k in which the anti-de Sitter space has been formed out of the worldvolume of the brane and the radial direction within T y 0 , and S k is the unit sphere within T y 0 .Maldacena's conjecture proposes that the M or string theory on this space AdS p+2 × S k , with N units of flux of the supergravity k-form field strength through S k , is dual to a specific conformal field theory on the boundary of AdS p+2 . The conjecture applies to the large N limit when a large number ...

We analyze in detail the moduli space of vacua of N =2 SUSY QCD with n c colors and n f flavors. The Coulomb branch has submanifolds with non-Abelian gauge symmetry.The massless quarks and gluons at these vacua are smoothly connected to the underlying elementary quarks and gluons. Upon breaking N =2 by an N =1 preserving mass term for the adjoint field the theory flows to N =1 SUSY QCD. Some of the massless quarks and gluons on the moduli space of the N =2 theory become the magnetic quarks and gluons of the N =1 theory. In this way we derive the duality in N =1 SUSY QCD by identifying its crucial building blocks-the magnetic degrees of freedom-using only semiclassical physics and the non-renormalization theorem. 3/96

We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety V or a Calabi-Yau hypersurface M ⊂ V . In the linear model the instanton moduli spaces are relatively simple objects and the correlators are explicitly computable; moreover, the instantons can be summed, leading to explicit solutions for both kinds of models. In the case of smooth V , our results reproduce and clarify an algebraic solution of the V model due to Batyrev. In addition, we find an algebraic relation determining the solution for M in terms of that for V . Finally, we propose a modification of the linear model which computes instanton expansions about any limiting point in the moduli space. In the smooth case this leads to a (second) algebraic solution of the M model. We use this description to prove some conjectures about mirror symmetry, including the previously conjectured "monomial-divisor mirror map" of Aspinwall, Greene, and Morrison. 12/94