N=2 Moduli Spaces and N=1 Dualities for SO(n_c) and USp(2n_c) SuperQCD

We determine the exact global structure of the moduli space of $N{=}2$ supersymmetric $SO(n)$ and \USp(2n) gauge theories with matter hypermultiplets in the fundamental representations, using the non-renormalization theorem for the Higgs branches and the exact solutions for the Coulomb branches. By adding an $(N{=}2)$--breaking mass term for the adjoint chiral field and varying the mass, the $N{=}2$ theories can be made to flow to either an ``electric'' $N{=}1$ supersymmetric QCD or its $N{=}1$ dual ``magnetic'' version. We thus obtain a derivation of the $N{=}1$ dualities of Seiberg.Comment: 20 pages, harvmac (b

On mixed phases in gauge theories

In many gauge theories at different values of parameters entering Lagrangian, the vacuum is dominated by coherent condensates of different mutually non-local fields (for instance, by condensates of electric or magnetic charges, or by various dyons). It is argued that the transition between these "dual to each other" phases proceeds through the intermediate "mixed phase", having qualitatively different features. The examples considered include: ordinary YM, N=1 SYM, N=1 SQCD, and broken N=2 SYM and SQCD.Comment: Latex, 19 pages; Talk given at "Continuous Advances in QCD-2002/Arkadyfest", honoring the 60-th birthday of Arkady Vainshtein; 17-23 May 2002, University of Minneapolis, Minnesota, USA; v.3: the extended and improved versio

Seiberg duality in three dimensions

We analyze three dimensional gauge theories with $Sp$ gauge group. We find that in some regime the theory should be described in terms of a dual theory, very much in the spirit of Seiberg duality in four dimensions. This duality does not coincide with mirror symmetry.Comment: 8 pages, LaTeX2e, using utarticle.cls (included

N=2 Electric-magnetic duality in a chiral background

We establish the consistency of duality transformations for generic systems of $N=2$ vector supermultiplets in the presence of a chiral background field. This is relevant, for instance, when dealing with spurion fields or when considering higher-derivative couplings of vector multiplets to supergravity. We point out that under duality most quantities do not transform as functions. With few exceptions, true functions are nonholomorphic, even though the duality transformations themselves are holomorphic in nature.Comment: LaTeX using espcrc2, 11 pp. To appear in proc. of the 29-th Int. Symp. Ahrenshoop, Bucko

Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus

We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirror pair. Furthermore, new pairs of conjugate models may be obtained by taking the product of old ones. We also give a sufficient (and possibly necessary) condition for two models to be conjugate, and show that it is satisfied by the mirror pairs proposed by one of the authors and~H\"ubsch.Comment: p.22, IASSNS-HEP-93/92, use harvma

A Generalized Construction of Mirror Manifolds

We generalize the known method for explicit construction of mirror pairs of $(2,2)$-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known.Comment: 16 page

Pursuing Gravitational S-Duality

Recently a strong-weak coupling duality in non-abelian non-supersymmetric theories in four dimensions has been found. An analogous procedure is reviewed, which allows to find the `dual action' to the gauge theory of dynamical gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\Theta$ term.Comment: Invited paper to appear in the special issue of the `Journal of Chaos, Solitons and Fractals' on: "Superstrings, M,F,S,... Theory" (M.S. El Naschie and C. Castro, editors), 19 pages, LaTeX file, no figure

Fusion Algebras of Fermionic Rational Conformal Field Theories via a Generalized Verlinde Formula

We prove a generalization of the Verlinde formula to fermionic rational conformal field theories. The fusion coefficients of the fermionic theory are equal to sums of fusion coefficients of its bosonic projection. In particular, fusion coefficients of the fermionic theory connecting two conjugate Ramond fields with the identity are either one or two. Therefore, one is forced to weaken the axioms of fusion algebras for fermionic theories. We show that in the special case of fermionic W(2,d)-algebras these coefficients are given by the dimensions of the irreducible representations of the horizontal subalgebra on the highest weight. As concrete examples we discuss fusion algebras of rational models of fermionic W(2,d)-algebras including minimal models of the $N=1$ super Virasoro algebra as well as $N=1$ super W-algebras SW(3/2,d).Comment: 28 pages (Plain TeX), BONN-HE-93-0

Some properties of unstable monopoles in Super-QCD

We study embeddings of the Prasad-Sommerfield monopole solution in SU(N) Super-QCD (N>2), where the role of the Higgs field is played by the squarks in the fundamental representation. Classically, the resulting configurations live in a phase with unbroken SU(k) subgroups of SU(N) (as a result they are not topologically stable). The structure of zero modes is such that they can be naturally interpreted as massive chiral superfields with R charge one and baryon number zero, transforming in the adjoint representation of a dual gauge group defined using the Goddard-Nuyts-Olive (GNO) framework. We discuss the possible applications of these monopoles to N=1 duality, and more generally the possibility of relating GNO-type dual gauge groups to those appearing in N=1 duality.Comment: 15 pages. harvma

Matrix Strings in Weakly Curved Background Fields

We investigate further the recent proposal for the form of the Matrix theory action in weak background fields. We perform DVV reduction to the multiple D0-brane action in order to find the Matrix string theory action for multiple fundamental strings in curved but weak NS-NS and R-R backgrounds. This matrix sigma model gives a definite prescription on how to deal with R-R fields with an explicit spacetime dependence in Type II string theory. We do this both via the 9-11 flip and the chain of T and S dualities, and further check on their equivalence explicitly. In order to do so, we also discuss the implementation of S-duality in the operators of the 2-dimensional world-volume supersymmetric gauge theory describing the Type IIB D-string. We compare the result to the known Green-Schwarz sigma model action (for one string), and use this comparison in order to discuss about possible, non-linear background curvature corrections to the Matrix string action (involving many strings), and therefore to the Matrix theory action. We illustrate the nonabelian character of our action with an example involving multiple fundamental strings in a non-trivial R-R flux, where the strings are polarized into a noncommutative configuration. This corresponds to a dielectric type of effect on fundamental strings.Comment: 46 pages, Latex; v2: added 3 refs and 1 commen