N=1 Super QCD and Fractional Branes

We show how to get the one-loop beta function and the chiral anomaly of N=1 Super QCD from a stack of fractional N D3-branes localized inside the world-volume of 2M fractional D7-branes on the orbifold C^3/(Z_2 x Z_2). They are obtained by analyzing the classical supergravity background generated by such a brane configuration, in the spirit of the gauge/gravity correspondence.Comment: 4 pages, LaTeX. Talk given at the IXth International Symposium on Particles, Strings and Cosmology PASCOS '03, Mumbai-India, January 3-8 2003. To appear in a special issue of Praman

D3-branes dynamics and black holes

Using the D3-brane as the fundamental tool, we adress two aspects of D-branes physics. The first regards the interaction between two electromagnetic dual D-branes in 10 dimensions. In particular, we give a meaning to {\it both} even and odd spin structure contributions, the latter being non vanishing for non zero relative velocity $v$ (and encoding the Lorentz-like contribution). The second aspect regards the D-brane/black holes correspondence. We show how the 4 dimensional configuration corresponding to a {\it single} D3-brane wrapped on the orbifold T^6/Z_3 represents a regular Reissner-Nordstrom solution of d=4 N=2 supergravityComment: 8 pages, latex, 1 eps figure. Talk presented by M. Bertolini at the conference "Quantum aspects of gauge theories, supergravity and unification" in Corfu`; to appear in the proceeding

More Anomalies from Fractional Branes

In this note we show how the anomalies of both pure and matter coupled N=1,2 supersymmetric gauge theories describing the low energy dynamics of fractional branes on orbifolds can be derived from supergravity.Comment: 11 pages, latex; v2: minor typos fixe

N=8 BPS black holes preserving 1/8 supersymmetry

In the context of N=8 supergravity we consider BPS black-holes that preserve 1/8 supersymmetry. It was shown in a previous paper that, modulo U-duality transformations of E_{7(7)} the most general solution of this type can be reduced to a black-hole of the STU model. In this paper we analize this solution in detail, considering in particular its embedding in one of the possible Special K\"ahler manifold compatible with the consistent truncations to N=2 supergravity, this manifold being the moduli space of the T^6/Z^3 orbifold, that is: SU(3,3)/SU(3)*U(3). This construction requires a crucial use of the Solvable Lie Algebra formalism. Once the group-theoretical analisys is done, starting from a static, spherically symmetric ans\"atz, we find an exact solution for all the scalars (both dilaton and axion-like) and for gauge fields, together with their already known charge-dependent fixed values, which yield a U-duality invariant entropy. We give also a complete translation dictionary between the Solvable Lie Algebra and the Special K\"ahler formalisms in order to let comparison with other papers on similar issues being more immediate. Although the explicit solution is given in a simplified case where the equations turn out to be more manageable, it encodes all the features of the more general one, namely it has non-vanishing entropy and the scalar fields have a non-trivial radial dependence.Comment: 29+1 pages, 1 Latex file; a misprint in the entropy formula, eq.(5.14), correcte

Worldsheet instantons and (0,2) linear models

We study the stability of heterotic compactifications described by (0,2) gauged linear sigma models with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of linear models for which a vanishing theorem holds, generating an extensive list of consistent heterotic backgrounds.Comment: 21 pages; v2: minor correction

A focus on focal surfaces

We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal surface (degree, class, class of its hyperplane section, sectional genus and degrees of the nodal and cuspidal curve). We study in particular the congruences of chords to a smooth curve and the congruences of bitangents or flexes to a smooth surface. We find that they possess unexpected components in their focal surface, and conjecture that they are the only ones with this property.Comment: Plain TeX, 33 pages with no figure

N=2 four-dimensional gauge theories from fractional branes

This is a pedagogical and extended version of the results published in Refs. [1,2] and presented by the authors in various talks during the last year. We discuss the type II D-branes (both regular and fractional) of the orbifold R^{1,5}*R^4/Z_2, we determine their corresponding supergravity solution and show how this can be used to study the properties of N=2 super Yang-Mills. Supergravity is able to reproduce the perturbative moduli space of the gauge theory, while it does not encode the non-perturbative corrections. The short distance region of space-time, which corresponds to the infrared region of the gauge theory, is excised by an enhancon mechanism, and more states should be included in the low energy effective action in order to enter inside the enhancon and recover the instanton corrections. (To be published on a Memorial Volume commemorating Michael Marinov)Comment: 44 pages, AMS-LaTeX, no figure