Is Strong Gravitational Radiation predicted by TeV-Gravity?

In TeV-gravity models the gravitational coupling to particles with energies E\sim m_{Pl} \sim 10 TeV is not suppressed by powers of ultra-small ratio E/M_{Pl} with M_{Pl} \sim 10^{19} GeV. Therefore one could imagine strong synchrotron radiation of gravitons by the accelerating particles to become the most pronounced manifestation of TeV-gravity at LHC. However, this turns out to be not true: considerable damping continues to exist, only the place of E/M_{Pl} it taken by a power of a ratio \theta\omega/E, where the typical frequency \omega of emitted radiation, while increased by a number of \gamma-factors, can not reach E/\vartheta unless particles are accelerated by nearly critical fields. Moreover, for currently available magnetic fields B \sim 10 Tesla, multi-dimensionality does not enhance gravitational radiation at all even if TeV-gravity is correct.Comment: 7 pages, LaTe

Horizontal-Branch Models and the Second-Parameter Effect. IV. The Case of M3 and Palomar 3

We present a detailed analysis of the "second-parameter pair" of globular clusters M3 (NGC 5272) and Palomar 3. Our main results can be summarized as follows: i) The horizontal-branch (HB) morphology of M3 is significantly bluer in its inner regions (observed with the Hubble Space Telescope) than in the cluster outskirts (observed from the ground), i.e., M3 has an internal second parameter. Most plausibly the mass loss on the red giant branch (RGB) has been more efficient in the inner than in the outer regions of the cluster. ii) The dispersion in mass of the Pal 3 HB is found to be very small -- consistent with zero -- and we argue that this is unlikely to be due to a statistical fluctuation. It is this small mass dispersion that leads to the most apparent difference in the HB morphologies of M3 and Pal 3. iii) The relative HB types of M3 and Pal 3, as measured by mean colors or parameters involving the number of blue, variable, and red HB stars, can easily be accounted for by a fairly small difference in age between these clusters, of order 0.5-1 Gyr -- which is in good agreement with the relative age measurement, based on the clusters' turnoffs, by VandenBerg (2000).Comment: 20 pages, 12 figures, emulateapj5 style. The Astrophysical Journal, in press. Figs. 1, 6, 9, 10 are in png format. The preprint (postscript format) with full resolution (embedded) figures is available from http://www.astro.virginia.edu/~mc6v

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE

Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble

The exact free energy of matrix model always obeys the Seiberg-Witten (SW) equations on a complex curve defined by singularities of the quasiclassical resolvent. The role of SW differential is played by the exact one-point resolvent. We show that these properties are preserved in generalization of matrix models to beta-ensembles. However, since the integrability and Harer-Zagier topological recursion are still unavailable for beta-ensembles, we need to rely upon the ordinary AMM/EO recursion to evaluate the first terms of the genus expansion. Consideration in this paper is restricted to the Gaussian model.Comment: 15 page

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the well-known Delzant construction of Hamiltonian toric manifolds. We establish the following topological properties of N: every N embeds as a submanifold in the corresponding moment-angle manifold Z, and every N is the total space of two different fibrations, one over the torus T^{m-n} with fibre a real moment-angle manifold R, and another over a quotient of R by a finite group with fibre a torus. These properties are used to produce new examples of Hamiltonian-minimal Lagrangian submanifolds with quite complicated topology.Comment: 14 pages, published version (minor changes

Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals

The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev matrix model (beta-ensemble) representations the latter being polylinear combinations of Selberg integrals. The "pure gauge" limit of these matrix models is, however, a non-trivial multiscaling large-N limit, which requires a separate investigation. We show that in this pure gauge limit the Selberg integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the Nekrasov function for pure SU(2) theory acquires a form very much reminiscent of the AMM decomposition formula for some model X into a pair of the BGW models. At the same time, X, which still has to be found, is the pure gauge limit of the elliptic Selberg integral. Presumably, it is again a BGW model, only in the Dijkgraaf-Vafa double cut phase.Comment: 21 page

Generalized matrix models and AGT correspondence at all genera

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2 gauge theory as the spectral curve of the generalized matrix model, thus providing a check of AGT correspondence at all genera.Comment: 19 pages; v2: version to appear in JHE

Mechanisms of arsenic clustering in silicon

A model of arsenic clustering in silicon is proposed and analyzed. The main feature of the proposed model is the assumption that negatively charged arsenic complexes play a dominant role in the clustering process. To confirm this assumption, electron density and concentration of impurity atoms incorporated into the clusters are calculated as functions of the total arsenic concentration. A number of the negatively charged clusters incorporating a point defect and one or more arsenic atoms are investigated. It is shown that for the doubly negatively charged clusters or for clusters incorporating more than one arsenic atom the electron density reaches a maximum value and then monotonically and slowly decreases as total arsenic concentration increases. In the case of doubly negatively charged cluster incorporating two arsenic atoms, the calculated electron density agrees well with the experimental data. Agreement with the experiment confirms the conclusion that two arsenic atoms participate in the cluster formation. Among all present models, the proposed model of clustering by formation of doubly negatively charged cluster incorporating two arsenic atoms gives the best fit to the experimental data and can be used in simulation of high concentration arsenic diffusion.Comment: 13 pages, 4 figures. Revised and shortened version of the paper has been published in Phys. Rev. B, Vol.74 (3), art. no. 035205 (2006

Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model

We find perfect agreements on the genus-one correction to the prepotential of SU(2) Seiberg-Witten theory with N_f=2, 3 between field theoretical and Dijkgraaf-Vafa-Penner type matrix model results.Comment: 12 pages; v2: minor revision; v3: more structured, submitted versio