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

Universal Correlators from Geometry

Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.Comment: 25 pages, 2 figure

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.

Spatially modulated instabilities of geometries with hyperscaling violation

We perform a study of possible instabilities of the infrared AdS(2) x R-2 region of solutions to Einstein-Maxwell-dilaton systems which exhibit an intermediate regime of hyperscaling violation and Lifshitz scaling. Focusing on solutions that are magnetically charged, we probe the response of the system to spatially modulated fluctuations, and identify regions of parameter space in which the infrared AdS(2) geometry is unstable to perturbations. The conditions for the existence of instabilities translate to restrictions on the structure of the gauge kinetic function and scalar potential. In turn, these can lead to restrictions on the dynamical critical exponent z and on the amount of hyperscaling violation theta. Our analysis thus provides further evidence for the notion that the true ground state of 'scaling' solutions with hyperscaling violation may be spatially modulated phases

Refined Chern-Simons theory and (q, t)-deformed Yang-Mills theory : Semi-classical expansion and planar limit

We study the relationship between refined Chern-Simons theory on lens spaces S-3/Z(p) and (q, t)-deformed Yang-Mills theory on the sphere S-2. We derive the instanton partition function of (q, t)-deformed U(N) Yang-Mills theory and describe it explicitly as an analytical continuation of the semi-classical expansion of refined Chern-Simons theory. The derivations are based on a generalization of the Weyl character formula to Macdonald polynomials. The expansion is used to formulate q-generalizations of beta-deformed matrix models for refined Chern-Simons theory, as well as conjectural formulas for the chi(y)-genus of the moduli space of U(N) instantons on the surface O(-p) -> P-1 for all p >= 1 which enumerate black hole microstates in refined topological string theory. We study the large N phase structures of the refined gauge theories, and match them with refined topological string theory on the resolved conifold

On the IR completion of geometries with hyperscaling violation

We study solutions to Einstein-Maxwell-dilaton gravity with a constant magnetic flux which describe, in the holographic AdS/CFT framework, field theories characterized by a dynamical critical exponent and a hyperscaling violation exponent. Such solutions are known to be IR-incomplete due to the presence of a running dilaton, which drives the theory towards strong coupling in the IR, where quantum corrections become important. After introducing generic corrections, in this note we examine the conditions for the emergence of an AdS_2 x R^2 region close to the horizon, which provides an IR-completion for the hyperscaling violating solutions. In the presence of these corrections, we construct explicit numerical solutions where the geometry flows from AdS_4 in the UV to AdS_2 x R^2 in the deep IR, with an intermediate region which exhbits both hyperscaling violation and Lifshitz scaling.We also provide constraints on the structure of Einstein-Maxwell-dilaton theories that admit such solutions, as well as an emergent AdS_2 x R^2 region in the infrared.Comment: Typos fixed, references added, improved discussio

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