Exact Superpotentials from Matrix Models

Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a large class of N=1 SUSY gauge theories can be extracted from the planar limit of a certain holomorphic matrix integral. We test their proposal against existing knowledge for a family of deformations of N=4 SUSY Yang-Mills theory involving an arbitrary polynomial superpotential for one of the three adjoint chiral superfields. Specifically, we compare the DV prediction for these models with earlier results based on the connection between SUSY gauge theories and integrable systems. We find complete agreement between the two approaches. In particular we show how the DV proposal allows the extraction of the exact eigenvalues of the adjoint scalar in the confining vacuum and hence computes all related condensates of the finite-N gauge theory. We extend these results to include Leigh-Strassler deformations of the N=4 theory.Comment: 28 pages, 1 figure, latex with JHEP.cls, replaced with typos corrected and one clarifying commen

Factors influencing the potency of marbofloxacin for pig pneumonia pathogens Actinobacillus pleuropneumoniae and Pasteurella multocida

For the pig respiratory tract pathogens, Actinobacillus pleuropneumoniae and Pasteurella multocida, Minimum Inhibitory Concentration (MIC) of marbofloxacin was determined in recommended broths and pig serum at three inoculum strengths. MICs in both growth matrices increased progressively from low, through medium to high starting inoculum counts, 104, 106 and 108 CFU/mL, respectively. P. multocida MIC ratios for high:low inocula were 14:4:1 for broth and 28.2:1 for serum. Corresponding MIC ratios for A. pleuropneumoniae were lower, 4.1:1 (broth) and 9.2:1 (serum). MIC high:low ratios were therefore both growth matrix and bacterial species dependent. The effect of alterations to the chemical composition of broths and serum on MIC were also investigated. Neither adjusting broth or serum pH in six increments over the range 7.0 to 8.0 nor increasing calcium and magnesium concentrations of broth in seven incremental steps significantly affected MICs for either organism. In time-kill studies, the killing action of marbofloxacin had the characteristics of concentration dependency against both organisms in both growth matrices. It is concluded that MIC and time-kill data for marbofloxacin, generated in serum, might be preferable to broth data, for predicting dosages of marbofloxacin for clinical use

Potency of marbofloxacin for pig pneumonia pathogens Actinobacillus pleuropneumoniae and Pasteurella multocida: Comparison of growth media

Pharmacodynamic properties of marbofloxacin were established for six isolates each of the pig respiratory tract pathogens, Actinobacillus pleuropneumoniae and Pasteurella multocida. Three in vitro indices of potency were determined; Minimum Inhibitory Concentration (MIC), Minimum Bactericidal Concentration (MBC) and Mutant Prevention Concentration (MPC). For MIC determination Clinical Laboratory Standards Institute guidelines were modified in three respects: (1) comparison was made between two growth media, an artificial broth and pig serum; (2) a high inoculum count was used to simulate heavy clinical bacteriological loads; and (3) five overlapping sets of two-fold dilutions were used to improve accuracy of determinations. Similar methods were used for MBC and MPC estimations. MIC and MPC serum:broth ratios for A. pleuropneumoniae were 0.79:1 and 0.99:1, respectively, and corresponding values for P. multocida were 1.12:1 and 1.32:1. Serum protein binding of marbofloxacin was 49%, so that fraction unbound (fu) serum MIC values were significantly lower than those predicted by correction for protein binding; fu serum:broth MIC ratios were 0.40:1 (A. pleuropneumoniae) and 0.50:1 (P. multocida). For broth, MPC:MIC ratios were 13.7:1 (A. pleuropneumoniae) and 14.2:1 (P. multocida). Corresponding ratios for serum were similar, 17.2:1 and 18.8:1, respectively. It is suggested that, for dose prediction purposes, serum data might be preferable to potency indices measured in broths

Instanton Effects in Three-Dimensional Supersymmetric Gauge Theories with Matter

Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that the asymptotic metric on the Coulomb branch coincides with the metric on Dancer's deformation of the monopole moduli space. For the N=2 theory with $N_f$ flavors, we compute the one-loop corrections to the metric and complex structure on the Coulomb branch. We then determine the superpotential including one-loop effects around the instanton background. These calculations provide an explicit check of several results previously obtained by symmetry and holomorphy arguments.Comment: 24 pages, Late

An Exact Elliptic Superpotential for N=1^* Deformations of Finite N=2 Gauge Theories

We study relevant deformations of the N=2 superconformal theory on the world-volume of N D3 branes at an A_{k-1} singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N=1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.Comment: 55 pages, 5 figures, latex with JHEP.cl

A New 2d/4d Duality via Integrability

We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional partition function in the Nekrasov-Shatashvili limit. At special quantized values of the Coulomb branch moduli, the saddle point condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain which coincides with the F-term equation of the dual two-dimensional theory. The on-shell values of the superpotential in the two theories are shown to coincide in corresponding vacua. We also identify two-dimensional duals for a large set of quiver gauge theories in four dimensions and generalize our proof to these cases.Comment: 19 pages, 2 figures, minor corrections and references adde

Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity properties of the eigenvalues. The methods are also used to examine further the pattern of eigenvalue degeneracies observed by Dorey et al. in [1,2].Comment: 22 pages, 13 figures. Added references, minor revision

S-duality of the Leigh-Strassler Deformation via Matrix Models

We investigate an exactly marginal N=1 supersymmetric deformation of SU(N) N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2,Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N=4 theory. We perform non-trivial tests of the matrix model results against semiclassical field theory analysis. We also show that there are interesting points in parameter space where condensates can diverge and vacua disappear. Based on the matrix model results, we propose an exact elliptic superpotential to describe the theory compactified on a circle of finite radius.Comment: 33 pages, 2 figures, uses JHEP.cls; minus sign typo corrected and 1 reference added, submitted to JHE

World-sheet Instantons via the Myers Effect and N=1^* Quiver Superpotentials

In this note we explore the stringy interpretation of non-perturbative effects in N=1^* deformations of the A_{k-1} quiver models. For certain types of deformations we argue that the massive vacua are described by Nk fractional D3-branes at the orbifold polarizing into k concentric 5-brane spheres each carrying fractional brane charge. The polarization of the D3-branes induces a polarization of D-instantons into string world-sheets wrapped on the Myers spheres. We show that the superpotentials in these models are indeed generated by these world-sheet instantons. We point out that for certain parameter values the condensates yield the exact superpotential for a relevant deformation of the Klebanov-Witten conifold theory.Comment: 24 pages, JHEP, some small errors and typos correcte

Massive Vacua of N=1* Theory and S-duality from Matrix Models

In this note we show how Dijkgraaf and Vafa's hypothesis relating the exact superpotential of an N=1 theory to a matrix model can be used to describe all the massive vacua of the N=1*, or mass deformed N=4, theory including the Higgs vacuum. The matrix model computation of the superpotential for each massive vacuum independently yields a modular function of the associated effective coupling in that vacuum which agrees with previously derived results up to a vacuum-independent additive constant. The results in the different massive vacua can be related by the action of SL(2,Z) on the N=4 coupling, thus providing evidence for modular invariance of the underlying N=4 theory.Comment: 9 pages, JHEP.cl