Exact Ground State Wave Functions for N Anyons in a Magnetic Field on a Torus

The complete set of ground state wave functions for N anyons in an external magnetic field on the torus is found. The cases when the filling factor is less than or equal to one are considered. The single valued description of anyons is employed through out by coupling bosons to a Chern-Simons field. At the end, the Chern-Simons interaction is removed by a singular gauge transformation as a result of which the wave functions become multi-component in agreement with other studies.Comment: 10 pages, Latex document, USITP-93-0

Some comments on N=2N=2 supersymmetric Yang-Mills

We comment on some aspects of the semiclassical BPS saturated states close to the curve $Im a_{D}/a =0$Comment: 8 pages, TEX, Harvma

G2G_2 holonomy metrics and wrapped D6-branes

We determine torsion class constraints for the supergravity background produced by D6-branes wrapping special Lagrangian cycles in a Calabi-Yau 3-fold. We employ a recently introduced method which involves probing the putative background by all possible supersymmetric brane configurations. We then lift this background to 11-dimensions to a product of 4-d Minkowski space and a 7-fold of G2-holonomy. The latter is a particular U(1) bundle over an almost complex manifold of SU(3) structure with specific torsion class constraints. We construct the closed 3- and 4-forms which calibrate the 3- and 4-cycles in the G2-holonomy manifold.Comment: 21 pages, references adde

Calibrations, Torsion Classes and Wrapped M-Branes

The present work has two goals. The first is to complete the classification of geometries in terms of torsion classes of M-branes wrapping cycles of a Calabi-Yau. The second goal is to give insight into the physical meaning of the torsion class constraints. We accomplish both tasks by defining new energy minimizing calibrations in M-brane backgrounds. When fluxes are turned on, it is these calibrations that are relevant, rather than those which had previously been defined in the context of purely geometric backgrounds

The geometry of wrapped M5-branes in Calabi-Yau 2-folds

We study the geometry of M5-branes wrapping a 2-cycle which is Special Lagrangian with respect to a specific complex structure in a Calabi-Yau two-fold. Using methods recently applied to the three-fold case, we are again able find a characterization of the geometry, in terms of a non-integrable almost complex structure and a (2,0) form. This time, however, due to the hyper-K{\"a}hler nature of the underlying 2-fold we also have the freedom of choosing a different almost complex structure with respect to which the wrapped 2-cycle is holomorphic. We show that this latter almost complex structure is integrable. We then relate our geometry to previously found geometries of M5-branes wrapping holomophic cycles and go further to prove some previously unknown results for M5-branes on holomorphic cycles

The Large N Limit of N=2,1{\cal N} =2,1 Field Theories from Threebranes in F-theory

We consider field theories arising from a large number of D3-branes near singularities in F-theory. We study the theories at various conformal points, and compute, using their conjectured string theory duals, their large $N$ spectrum of chiral primary operators. This includes, as expected, operators of fractional conformal dimensions for the theory at Argyres-Douglas points. Additional operators, which are charged under the (sometimes exceptional) global symmetries of these theories, come from the 7-branes. In the case of a $D_4$ singularity we compare our results with field theory and find agreement for large $N$. Finally, we consider deformations away from the conformal points, which involve finding new supergravity solutions for the geometry produced by the 3-branes in the 7-brane background. We also discuss 3-branes in a general background.Comment: 24 pages. Uses Harvmac. v2: reference adde

One dimensional M5-brane intersections

We study one dimensional intersections of M5 branes with M5 and M2 branes. On the worldvolume of the M5-brane, such an intersection appears as a string soliton. We study this worldvolume theory in two different regimes: 1) Where the worldvolume theory is formulated in flat space and 2) where the worldvolume theory is studied in the supergravity background produced by a stack of M5 (or M2) branes. In both cases, we study the corresponding string solitons, and find the most general BPS configuration consistent with the fraction of supersymmetries preserved. We argue that M5 and M2 brane intersections leave different imprints on the worldvolume theory of the intersecting probe brane, although geometrically they appear to be similar.Comment: 13 pages, LaTeX, references adde