Hybridization of institutions

Extended version including all proofsModal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification. In this context, the first contribution of this paper is an attempt to ‘universalize’ the hybridization idea. Following the lines of [DS07], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institution-independent level. The method extends arbitrary institutions with Kripke semantics (for multi-modalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (FOL) deter- mines a comorphism from its hybridization to FOL. This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features.Fundação para a Ciência e a Tecnologia (FCT

Quantization of the Chern-Simons Coupling Constant

We investigate the quantum consistency of p-form Maxwell-Chern-Simons electrodynamics in 3p+2 spacetime dimensions (for p odd). These are the dimensions where the Chern--Simons term is cubic, i.e., of the form FFA. For the theory to be consistent at the quantum level in the presence of magnetic and electric sources, we find that the Chern--Simons coupling constant must be quantized. We compare our results with the bosonic sector of eleven dimensional supergravity and find that the Chern--Simons coupling constant in that case takes its corresponding minimal allowed value.Comment: 15 pages, 1 figure, JHEP3.cls. Equation (8.6) corrected and perfect agreement with previous results is obtaine

The Ruled Vertex and Nontoric del Pezzo Surfaces

We construct the topological partition function of local nontoric del Pezzo surfaces using the ruled vertex formalism.Comment: 16 pages, 4 figure

Geometric transitions and integrable systems

We consider {\bf B}-model large $N$ duality for a new class of noncompact Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a Calabi-Yau threefold. The closed string side of the transition is governed at genus zero by an $A_1$ Hitchin integrable system on a genus $g$ Riemann surface $\Sigma$. The open string side is described by a holomorphic Chern-Simons theory which reduces to a generalized matrix model in which the eigenvalues lie on the compact Riemann surface $\Sigma$. We show that the large $N$ planar limit of the generalized matrix model is governed by the same $A_1$ Hitchin system therefore proving genus zero large $N$ duality for this class of transitions.Comment: 70 pages, 1 figure; version two: minor change

Meta-Stable Dynamical Supersymmetry Breaking Near Points of Enhanced Symmetry

We show that metastable supersymmetry breaking is generic near certain enhanced symmetry points of gauge theory moduli spaces. Our model consists of two sectors coupled by a singlet and combines dynamical supersymmetry breaking with an O'Raifeartaigh mechanism in terms of confined variables. All relevant mass parameters, including the supersymmetry breaking scale, are generated dynamically. The metastable vacua appear as a result of a balance between non-perturbative and perturbative quantum effects along a pseudo-runaway direction.Comment: 27 pages, harvmac, 6 figure

Reaction of Group III Biheterocyclic Complexes

Group III alkyl complexes supported by a ferrocene diamide ligand (1,1′-fc(NSitBuMe_2)_2) have been found to be reactive toward aromatic N-heterocycles such as 1-methylimidazole and pyridines. These reactions were investigated experimentally and computationally. An initial C−H activation event is followed by a coupling reaction to form biheterocyclic complexes, in which one of the rings is dearomatized. In the case of 1-methylimidazole, the biheterocyclic compound could not be isolated and further led to an imidazole ring-opened product; in the case of pyridines, it transformed into an isomer with extended conjugation of double bonds. Mechanisms for both reactions are proposed on the basis of experimental and computational results. DFT calculations were also used to show that an energetically accessible pathway for the ring-opening of pyridines exists

A Non-Renormalization Theorem for the d=1, N=8 Vector Multiplet

Sigma models describing low energy effective actions on D0-brane probes with N=8 supercharges are studied in detail using a manifestly d=1, N=4 super-space formalism. Two 0+1 dimensional N=4 multiplets together with their general actions are constructed. We derive the condition for these actions to be N=8 supersymmetric and apply these techniques to various D-brane configurations. We find that if in addition to N=8 supersymmetry the action must also have Spin(5) invariance, the form of the sigma model metric is uniquely determined by the one-loop result and is not renormalized perturbatively or non-perturbatively.Comment: Uses harvmac, 16 pages. We correct an error pointed out by E. Witte

Fractional two-branes, toric orbifolds and the quantum McKay correspondence

We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of orbifolds C^3/Z_n. We study a generalisation of the McKay correspondence proposed in hep-th/0504164 called the quantum McKay correspondence by constructing duals to the fractional two-branes. Details are explicitly worked out for two examples -- the crepant resolutions of C^3/Z_3 and C^3/Z_5.Comment: 34 pages, 2 figures, LaTeX (JHEP3 style); (v2) typos corrected; (v3) sec 3 reorganise

Matrix Models, Topological Strings, and Supersymmetric Gauge Theories

We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.Comment: 22 pages, minor correction