Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory

We derive the analog of the large $N$ Gross-Taylor holomorphic string expansion for the refinement of $q$-deformed $U(N)$ Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of $q$-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit $q=1$, the expansion defines a new $\beta$-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit $\beta=1$ to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and $\beta$-ensembles of matrix models arising in refined topological string theory.Comment: 45 pages; v2: References adde

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

N=1* vacua, Fuzzy Spheres and Integrable Systems

We calculate the exact eigenvalues of the adjoint scalar fields in the massive vacua of N=1* SUSY Yang-Mills with gauge group SU(N). This provides a field theory prediction for the distribution of D3 brane charge in the AdS dual. We verify the proposal of Polchinski and Strassler that the D3-brane's lie on a fuzzy sphere in the supergravity limit and determine the corrections to this distribution due to worldsheet and quantum effects. The calculation also provides several new results concerning the equilibrium configurations of the N-body Calogero-Moser Hamiltonian.Comment: 20 page

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

G2 Hitchin functionals at one loop

We consider the quantization of the effective target space description of topological M-theory in terms of the Hitchin functional whose critical points describe seven-manifolds with G2 structure. The one-loop partition function for this theory is calculated and an extended version of it, that is related to generalized G2 geometry, is compared with the topological G2 string. We relate the reduction of the effective action for the extended G2 theory to the Hitchin functional description of the topological string in six dimensions. The dependence of the partition functions on the choice of background G2 metric is also determined.Comment: 58 pages, LaTeX; v2: Acknowledgments adde

Cancer vaccines with emphasis on a viral oncolysate melanoma vaccine

Biotherapy of malignant diseases has become the fourth treatment modality besides surgery, chemo- and radiotherapy. Whole cell melanoma vaccines with or without BCG and other adjuvants, purified ganglioside and shed antigens, recombinant viruses carrying tumor antigens, dendritic cells pulsed with antigenic peptides etc. are in clinical trials.Efficacious viral oncolysate vaccines induce the host to mount tumor-specific cytotoxic T-cell response and prevention of relapses is supported by clinical trials. The use of „polyvalent” whole cell vaccines vs. purified or genetically engineered single antigen vaccines is justified asi.only very few single tumor antigens are present in all tumors of a given histological type; andii.antigen modulation occurs in tumors rendering them resistant to immune attack generated by vaccine against a single antigen. Thus polyvalent vaccines immunize against several antigens vs. against a selected antigen

Invariant Differential Operators and Characters of the AdS_4 Algebra

The aim of this paper is to apply systematically to AdS_4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS_4 algebra and group. We give explicitly all singular (null) vectors of the reducible AdS_4 Verma modules. These are used to obtain the AdS_4 invariant differential operators. Using this we display a new structure - a diagram involving four partially equivalent reducible representations one of which contains all finite-dimensional irreps of the AdS_4 algebra. We study in more detail the cases involving UIRs, in particular, the Di and the Rac singletons, and the massless UIRs. In the massless case we discover the structure of sets of 2s_0-1 conserved currents for each spin s_0 UIR, s_0=1,3/2,... All massless cases are contained in a one-parameter subfamily of the quartet diagrams mentioned above, the parameter being the spin s_0. Further we give the classification of the so(5,C) irreps presented in a diagramatic way which makes easy the derivation of all character formulae. The paper concludes with a speculation on the possible applications of the character formulae to integrable models.Comment: 30 pages, 4 figures, TEX-harvmac with input files: amssym.def, amssym.tex, epsf.tex; version 2 1 reference added; v3: minor corrections; v.4: minor corrections, v.5: minor corrections to conform with version in J. Phys. A: Math. Gen; v.6.: small correction and addition in subsections 4.1 & 4.

The effect of low temperature and low light intensity on nutrient removal from municipal wastewater by purple phototrophic bacteria (PPB)

There has been increased interest in alternative wastewater treatment systems to improve nutrient recovery while achieving acceptable TCOD, TN, and TP discharge limits. Purple phototrophic bacteria (PPB) have a high potential for simultaneous nutrient removal and recovery from wastewater. This study evaluated the PPB performance and its growth at different operating conditions with a focus on HRT and light optimization using a continuous-flow membrane photobioreactor (PHB). Furthermore, the effect of low temperature on PPB performance was assessed to evaluate the PPB’s application in cold-climate regions. In order to evaluate PPB performance, TCOD, TN, and TP removal efficiencies and Monod kinetic parameters were analyzed at different HRTs (36, 18, and 9 h), at temperatures of 22°C and 11°C and infrared (IR) light intensities of 50, 3, and 1.4 Wm-2. The results indicated that low temperature had no detrimental impact on PPB’s performance. The photobioreactor (PHB) with cold-enriched PPB has a high potential to treat municipal wastewater with effluent concentrations below target limits (TCOD˂ 50mgL-1, TN˂10 mgL-1, and TP˂1 mgL-1). Monod kinetic parameters Ks, K, Y, and Kd were estimated at 20-29 mgCODL-1, 1.6-1.9 mgCOD(mgVSS.d)-1, 0.47 mgVSS mgCOD-1, and 0.07-0.08 d-1 at temperatures of 11°C-22°C respectively. The results of the steady-state mass balances showed TCOD, TN, and TP recoveries of 80%-86%, which reflected PPB’s substrate and nutrient assimilation. Previous studies utilized high light intensities (˃ 50 Wm-2) to provide PPB with the maximum energy required for its growth. In order to enable the PPB technology as a practical approach in municipal wastewater treatment, light intensity must be optimized. Based on the literature, there is no study on PPB performance at low light intensities using a continuous-flow membrane photobioreactor. The effect of low light intensities of 3, and 1.4 Wm-2 on PPB performance was addressed in this study. The results indicated that PPB at a light intensity as low as 1.4 Wm-2 were able to treat municipal wastewater with effluent concentrations below above-mentioned target limits. Light intensity (1-50 Wm-2) had no detrimental impact on PPB performance and Monod kinetic parameters. This study showed that the optimized light intensity required for municipal wastewater treatment with PPB is significantly lower than previously indicated in the literature. The energy consumptions attributed to PHB’s illumination of 3, and 1.4 Wm-2 were determined to be 1.44, and 0.67 kWh/m3 which is significantly lower than previous studies (˃ 24 kWh/m3)

Instanton Counting and Wall-Crossing for Orbifold Quivers

Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative {Mathematical expression} gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated with the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge theory variables and orbifold data. We introduce the notion of virtual instanton quiver associated with the natural symplectic charge lattice which governs the quantum wall-crossing behaviour of BPS states in this context. The McKay correspondence naturally connects our formalism with other approaches to wall-crossing based on quantum monodromy operators and cluster algebras

Instantons, Quivers and Noncommutative Donaldson-Thomas Theory

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.Comment: 95 pages, 5 figures; v2: clarifying comments added, discussions using tilting strengthened, references added and updated; v3: minor corrections, final version to be published in Nuclear Physics