Non-perturbative studies of N=2 conformal quiver gauge theories

We study N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n=1,2, also in the presence of an Omega-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotential a la Nekrasov using localization methods.Comment: 56 pages, 7 figures, PdfLaTeX. v2: a few references added, version to appear on Fortschritte der Physi

Modular and duality properties of surface operators in N=2* gauge theories

We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure N=2 or to N=2* gauge theories.Comment: 51 pages, v3: references added, typos fixed, footnote added, some small changes in the text, appendix B streamlined. Matches the published versio

SONTRAC—a scintillating plastic fiber tracking detector for neutron and proton imaging spectroscopy

SONTRAC (SOlar Neutron TRACking imager and spectrometer) is a conceptual instrument intended to measure the energy and incident direction of 20–150 MeV neutrons produced in solar flares. The intense neutron background in a low-Earth orbit requires that imaging techniques be employed to maximize an instrument’s signal-to-noise ratio. The instrument is comprised of mutually perpendicular, alternating layers of parallel, scintillating, plastic fibers that are viewed by optoelectronic devices. Two stereoscopic views of recoil proton tracks are necessary to determine the incident neutron’s direction and energy. The instrument can also be used as a powerful energetic proton imager. Data from a fully functional 3-d prototype are presented. Early results indicate that the instrument’s neutron energy resolution is approximately 10% with the neutron incident direction determined to within a few degrees

The adenomatous polyposis coli protein unambiguously localizes to microtubule plus ends and is involved in establishing parallel arrays of microtubule bundles in highly polarized epithelial cells

Loss of full-length adenomatous polyposis coli (APC) protein correlates with the development of colon cancers in familial and sporadic cases. In addition to its role in regulating β-catenin levels in the Wnt signaling pathway, the APC protein is implicated in regulating cytoskeletal organization. APC stabilizes microtubules in vivo and in vitro, and this may play a role in cell migration (Näthke, I.S., C.L. Adams, P. Polakis, J.H. Sellin, and W.J. Nelson. 1996. J. Cell Biol. 134:165–179; Mimori-Kiyosue, Y., N. Shiina, and S. Tsukita. 2000. J. Cell Biol. 148:505–517; Zumbrunn, J., K. Inoshita, A.A. Hyman, and I.S. Näthke. 2001. Curr. Biol. 11:44–49) and in the attachment of microtubules to kinetochores during mitosis (Fodde, R., J. Kuipers, C. Rosenberg, R. Smits, M. Kielman, C. Gaspar, J.H. van Es, C. Breukel, J. Wiegant, R.H. Giles, and H. Clevers. 2001. Nat. Cell Biol. 3:433–438; Kaplan, K.B., A. Burds, J.R. Swedlow, S.S. Bekir, P.K. Sorger, and I.S. Näthke. 2001. Nat. Cell Biol. 3:429–432). The localization of endogenous APC protein is complex: actin- and microtubule-dependent pools of APC have been identified in cultured cells (Näthke et al., 1996; Mimori-Kiyosue et al., 2000; Reinacher-Schick, A., and B.M. Gumbiner. 2001. J. Cell Biol. 152:491–502; Rosin-Arbesfeld, R., G. Ihrke, and M. Bienz. 2001. EMBO J. 20:5929–5939). However, the localization of APC in tissues has not been identified at high resolution. Here, we show that in fully polarized epithelial cells from the inner ear, endogenous APC protein associates with the plus ends of microtubules located at the basal plasma membrane. Consistent with a role for APC in supporting the cytoskeletal organization of epithelial cells in vivo, the number of microtubules is significantly reduced in apico-basal arrays of microtubule bundles isolated from mice heterozygous for APC

Surface operators in 5d gauge theories and duality relations

We study half-BPS surface operators in 5d N=1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.Comment: 39 pages. v2: A few sentences rephrased, references added, and typos corrected. Matches version published in JHE

A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD

The Schrodinger wave functional for the d=3+1 SU(N) vacuum is a partition function constructed in d=4; the exponent 2S in the square of the wave functional plays the role of a d=3 Euclidean action. We start from a gauge-invariant conjecture for the infrared-dominant part of S, based on dynamical generation of a gluon mass M in d=4. We argue that the exact leading term, of O(M), in an expansion of S in inverse powers of M is a d=3 gauge-invariant mass term (gauged non-linear sigma model); the next leading term, of O(1/M), is a conventional Yang-Mills action. The d=3 action that is the sum of these two terms has center vortices as classical solutions. The d=3 gluon mass, which we constrain to be the same as M, and d=3 coupling are related through the conjecture to the d=4 coupling strength, but at the same time the dimensionless ratio in d=3 of mass to coupling squared can be estimated from d=3 dynamics. This allows us to estimate the QCD coupling $\alpha_s(M^2)$ in terms of this strictly d=3 ratio; we find a value of about 0.4, in good agreement with an earlier theoretical value but a little low compared to QCD phenomenology. The wave functional for d=2+1 QCD has an exponent that is a d=2 infrared-effective action having both the gauge-invariant mass term and the field strength squared term, and so differs from the conventional QCD action in two dimensions, which has no mass term. This conventional d=2 QCD would lead in d=3 to confinement of all color-group representations. But with the mass term (again leading to center vortices), N-ality = 0 mod N representations are not confined.Comment: 15 pages, no figures, revtex

Noncanonical Quantization of Gravity. I. Foundations of Affine Quantum Gravity

The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel Hilbert space. Constraints are introduced following the projection operator method which involves no gauge fixing, no complicated moduli space, nor any auxiliary fields. The result, which is only qualitatively sketched in the present paper, involves another reproducing kernel with which inner products are defined for the physical Hilbert space and which is obtained through a reduction of the original reproducing kernel. Several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one-dimensional quantum mechanical models. These toy models help in motivating and understanding the analysis in the case of gravity.Comment: minor changes, LaTeX, 37 pages, no figure

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)South Asia, South Asia and Central Asia, Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

Fundamental solutions of Dirac type operators are introduced for a class of conformally. at spin manifolds. This class consists of manifolds obtained by factoring out the upper half-space of R-n by congruence subgroups of generalized modular groups. Basic properties of these fundamental solutions are presented together with associated Eisenstein and Poincare type series