Holography and CFT on Generic Manifolds

In this paper it is shown how the AdS/CFT correspondence extends to a more general situation in which the first theory is defined on (d+1)-dimensional manifold $\tilde M$ defined as the filling in of a compact d-dimensional manifold M. The stability of the spectral correspondence mass/conformal-weight under such geometry changes is also proven.Comment: 8+1 pages, no figures, misprints correcte

Superdevelopments for Weak Reduction

We study superdevelopments in the weak lambda calculus of Cagman and Hindley, a confluent variant of the standard weak lambda calculus in which reduction below lambdas is forbidden. In contrast to developments, a superdevelopment from a term M allows not only residuals of redexes in M to be reduced but also some newly created ones. In the lambda calculus there are three ways new redexes may be created; in the weak lambda calculus a new form of redex creation is possible. We present labeled and simultaneous reduction formulations of superdevelopments for the weak lambda calculus and prove them equivalent

The Instanton Universal Moduli Space of N=2 Supersymmetric Yang-Mills Theory

We use the recursive structure of the compactification of the instanton moduli space of N=2 Super Yang-Mills theory with gauge group SU(2), to construct, by inductive limit, a universal moduli space which includes all the multi-instanton moduli spaces. Furthermore, with the aim of understanding the field theoretic structure of the strong coupling expansion, we perform the Borel sum which acts on the parameter defining such a universal moduli space.Comment: 1+4 pages, LaTeX. Minor changes. To appear in Phys. Lett.

Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings

We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.Comment: 17 page

The geometry of the M5-branes and TQFTs

The calculation of the partition function for N M5-branes is addressed for the case in which the worldvolume wraps a manifold $T^2\times M_4$, where $M_4$ is simply connected and Kaehler. This is done in a compactification of M-theory which induces the Vafa-Witten theory on $M_4$ in the limit of vanishing torus volume. The results follow from the equivalence of the BPS spectrum counting in the complementary limit of vanishing $M_4$ volumes and from a classification of the the moduli space of quantum vacua of the supersymmetric twisted theory in terms of associated spectral covers. This reduces the problem of the moduli counting to algebraic equations.Comment: 17+1 pages, LaTeX file; v2 misprints corrected and clarifications added, final version to appear in Journal of Geometry and Physic

The M5-brane on K3 and del Pezzo's and multi-loop string amplitudes

We study the BPS spectrum of Little String Theory for bound states of M5-branes wrapped on six manifold of product topology $M_4\times\Sigma_2$ and the apparence of multi-loop $\theta$-functions in a supersymmetric index calculation. We find a total reconstruction of the g-loop heterotic contribution in the case of a double K3 M-theory compactification. Moreover, we consider total wrapping of M5-branes on del Pezzo surfaces $B_k$ and, by studying the relevant amplitude, we notice the arising of $\theta$-functions relative to BPS strings on $T^{k-1}$, i.e. membranes on $T^k$. This happens because of beautiful relations between four dimensional SYM theories and CFTs in two dimensions and seems to be linked to a duality recently observed by A.Iqbal, A.Neitzke and C.Vafa in.Comment: 1+14 pages; v2: misprints corrected, clarifications and one reference adde

On The Beta-Function in N=2 Supersymmetric Yang-Mills Theory

The constraints of N=2 supersymmetry, in combination with several other quite general assumptions, have recently been used to show that N=2 supersymmetric Yang-Mills theory has a low energy quantum parameter space symmetry characterised by the discrete group \gu. We show that if one also assumes the commutativity of renormalization group flow with the action of this group on the complexified coupling constant \ta, then this is sufficient to determine the non-perturbative $\beta$-function, given knowledge of its weak coupling behaviour. The result coincides with the outcome of direct calculations from the Seiberg-Witten solution.Comment: 10 pages, analysis in section 3 modified, to appear in Phys. Lett.

Conifold geometries, matrix models and quantum solutions

This paper is a continuation of hepth/0507224 where open topological B-models describing D-branes on 2-cycles of local Calabi--Yau geometries with conical singularities were studied. After a short review, the paper expands in particular on two aspects: the gauge fixing problem in the reduction to two dimensions and the quantum matrix model solutions.Comment: 17 p. To appear in proc. Symposium QTS-4, Varna (Bulgaria), August 200

Matrix String Theory, 2D SYM Instantons and affine Toda systems

Extending a recent result of S.B. Giddings, F. Hacquebord and H. Verlinde, we show that in the U(N) SYM Matrix theory there exist classical BPS instantons which interpolate between different closed string configurations via joining/splitting interactions similar to those of string field theory. We construct them starting from branched coverings of Riemann surfaces. For the class of them which we analyze in detail the construction can be made explicit in terms U(N) affine Toda field theories.Comment: 12 pages, 1 eps figure, JHEP.cls LaTeX2e class file; sign corrected, ref. and acknowledgements update