2,574 research outputs found
On the Moduli Space of SU(3) Seiberg-Witten Theory with Matter
We present a qualitative model of the Coulomb branch of the moduli space of
low-energy effective N=2 SQCD with gauge group SU(3) and up to five flavours of
massive matter. Overall, away from double cores, we find a situation broadly
similar to the case with no matter, but with additional complexity due to the
proliferation of extra BPS states. We also include a revised version of the
pure SU(3) model which can accommodate just the orthodox weak coupling
spectrum.Comment: 32 pages, 25 figures, uses JHEP.cls, added references, deleted joke
Issues in the design and implentation of an R&D tax credit for the UK
R&D tax credits have become a popular policy tool for encouraging research and development (R&D) spending by business, with many countries offering subsidies of this form. The divergence between private and social rates of return to R&D expenditure by private firms provides one of the main justifications for government subsidies to R&D.2 In order to achieve the optimal level of R&D investment, government policy aims to bring private incentives in line with the social rate of return. An R&D tax credit does this by reducing the cost to the firm of doing R&D. Recent empirical evidence suggests that R&D tax credits are an effective instrument in stimulating additional R&D. However, in order to be desirable, a policy needs to be cost-effective and implementable.
This Briefing Note reviews some of the major issues in the design and implementation of R&D tax credits. In Section 2, we briefly discuss the existing tax treatment of R&D in the UK. In particular, we outline the new Research and Development Allowance - which is an allowance for expenditure on plant, machinery and buildings for use in scientific research and which is available to firms of all sizes - and the tax credit for R&D that is available to small and medium-sized enterprises (SMEs). We then discuss, in Section 3, some of the main design features of tax credits that have been implemented in other countries. The discussion mainly concerns the question of how to target new or incremental R&D so as to keep down the total exchequer cost. We discuss problems that arise in defining incremental R&D and how these can be tackled. In Section 4, we provide estimates of the amount of new R&D and the exchequer cost that would be likely to result from implementing different designs of R&D tax credit in the UK. Section 5 concludes. Some technical details are dealt with in the Appendix
Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms
We identify the spectral curve of pure gauge SU(2) Seiberg-Witten theory with
the Weierstrass curve \mathbbm{C}/L \ni z \mapsto (1,\wp(z),\wp(z)') and
thereby obtain explicitely a modular form from which the moduli space parameter
and lattice parameters , can be derived in terms of modular
respectively theta functions. We further discuss its relationship with the
triplet model conformal field theory.Comment: 11 + 2 pages, no figures, shortened, to be published in jm
Holomorphic Anomaly in Gauge Theories and Matrix Models
We use the holomorphic anomaly equation to solve the gravitational
corrections to Seiberg-Witten theory and a two-cut matrix model, which is
related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local
Calabi-Yau manifold. In both cases we construct propagators that give a
recursive solution in the genus modulo a holomorphic ambiguity. In the case of
Seiberg-Witten theory the gravitational corrections can be expressed in closed
form as quasimodular functions of Gamma(2). In the matrix model we fix the
holomorphic ambiguity up to genus two. The latter result establishes the
Dijkgraaf-Vafa conjecture at that genus and yields a new method for solving the
matrix model at fixed genus in closed form in terms of generalized
hypergeometric functions.Comment: 34 pages, 2 eps figures, expansion at the monopole point corrected
and interpreted, and references adde
Skyrmion and Skyrme-Black holes in de Sitter spacetime
Numerical arguments are presented for the existence of regular and black hole
solutions of the Einstein-Skyrme equations with a positive cosmological
constant. These classical configurations approach asymptotically the de Sitter
spacetime. The main properties of the solutions and the differences with
respect to the asymptotically flat ones are discussed. It particular our
results suggest that, for a positive cosmological constant, the mass evaluated
as timelike infinity in infinite. Special emphasis is set to De Sitter black
holes Skyrmions which display two horizons.Comment: 11 pages, 4 figure
Epidemic threshold in structured scale-free networks
We analyze the spreading of viruses in scale-free networks with high
clustering and degree correlations, as found in the Internet graph. For the
Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a
phase transition at a finite threshold of the transmission probability.
Comparing with the absence of a finite threshold in networks with purely random
wiring, our result suggests that high clustering and degree correlations
protect scale-free networks against the spreading of viruses. We introduce and
verify a quantitative description of the epidemic threshold based on the
connectivity of the neighborhoods of the hubs.Comment: 4 pages, 4 figure
The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
We present an exact description of the metric on the moduli space of vacua
and the spectrum of massive states for four dimensional N=2 supersymmetric
SU(n) gauge theories. The moduli space of quantum vacua is identified with the
moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde
Discriminating spin through quantum interference
Many of the proposed solutions to the hierarchy and naturalness problems
postulate new `partner' fields to the standard model particles. Determining the
spins of these new particles will be critical in distinguishing among the
various possible SM extensions, yet proposed methods rely on the underlying
models. We propose a new model-independent method for spin measurements which
takes advantage of quantum interference among helicity states. We demonstrate
that this method will be able to discriminate scalar particles from higher spin
states at the ILC, and discuss application to higher spins and possible uses at
the LHC.Comment: 11 pages, 11 figure
Time Correlation Functions of Three Classical Heisenberg Spins on an Isosceles Triangle and on a Chain: Strong Effects of Broken Symmetry
At arbitrary temperature , we solve for the dynamics of single molecule
magnets composed of three classical Heisenberg spins either on a chain with two
equal exchange constants , or on an isosceles triangle with a third,
different exchange constant . As T\rightrarrow\infty, the Fourier
transforms and long-time asymptotic behaviors of the two-spin time correlation
functions are evaluated exactly. The lack of translational symmetry on a chain
or an isosceles triangle yields time correlation functions that differ
strikingly from those on an equilateral trinagle with . At low ,
the Fourier transforms of the two autocorrelation functions with
show one and four modes, respectively. For a semi-infinite range, one
mode is a central peak. At the origin of this range, this mode has a novel
scaling form.Comment: 9 pages, 14 figures, accepted for publication in Phys. Rev.
Topological Strings and (Almost) Modular Forms
The B-model topological string theory on a Calabi-Yau threefold X has a
symmetry group Gamma, generated by monodromies of the periods of X. This acts
on the topological string wave function in a natural way, governed by the
quantum mechanics of the phase space H^3(X). We show that, depending on the
choice of polarization, the genus g topological string amplitude is either a
holomorphic quasi-modular form or an almost holomorphic modular form of weight
0 under Gamma. Moreover, at each genus, certain combinations of genus g
amplitudes are both modular and holomorphic. We illustrate this for the local
Calabi-Yau manifolds giving rise to Seiberg-Witten gauge theories in four
dimensions and local P_2 and P_1 x P_1. As a byproduct, we also obtain a simple
way of relating the topological string amplitudes near different points in the
moduli space, which we use to give predictions for Gromov-Witten invariants of
the orbifold C^3/Z_3.Comment: 62 pages, 1 figure; v2: minor correction
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