78 research outputs found
Symplectic leaves of W-algebras from the reduced Kac-Moody point of view
The symplectic leaves of W-algebras are the intersections of the symplectic
leaves of the Kac-Moody algebras and the hypersurface of the second class
constraints, which define the W-algebra. This viewpoint enables us to classify
the symplectic leaves and also to give a representative for each of them. The
case of the (W_{2}) (Virasoro) algebra is investigated in detail, where the
positivity of the energy functional is also analyzed.Comment: Latex, 6 pages, Talk presented by Z. Bajnok at the Second
International Conference on Geometry, Integrability and Quantization, Varna,
200
On the charge density and asymptotic tail of a monopole
We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1/r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions. (C) 2016 AIP Publishing LLC
Geometric quantization of the global Liouville mechanics
The reduced SL(2,R) WZW quantum mechanics is analysed in the framework of
geometric quantization. The spectrum of the Hamiltonian is determined, and it
is found, that contrary to the previous approaches, there is a unique,
physically preferred quantisation of the system.Comment: 5 pages, LaTe
QCD thermodynamics with dynamical overlap fermions
We study QCD thermodynamics using two flavors of dynamical overlap fermions
with quark masses corresponding to a pion mass of 350 MeV. We determine several
observables on N_t=6 and 8 lattices. All our runs are performed with fixed
global topology. Our results are compared with staggered ones and a nice
agreement is found.Comment: 14 pages, 6 figures, 1 tabl
Radius of convergence in lattice QCD at finite μB with rooted staggered fermions
In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity eμ/T. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around μ=0. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We show that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. This is a cutoff effect that potentially affects all estimates of the radius of convergence with the standard staggered rooting. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial and, therefore, of the numerical study of Lee-Yang zeros. We also describe an algorithm to determine the Lee-Yang zeros and apply it to configurations generated with the 2-stout improved staggered action at Nt=4. We perform a finite-volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence of the Taylor expansion extrapolated to an infinite volume. We show that the limiting singularity is not on the real line, thus giving a lower bound on the location of any possible phase transitions at this lattice spacing. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be μB/T≈2 and roughly temperature independent. Our simulations are performed at strange quark chemical potential μs=0, but the method can be straightforwardly extended to strangeness chemical potential μS=0 or strangeness neutrality
Axion cosmology, lattice QCD and the dilute instanton gas
Axions are one of the most attractive dark matter candidates. The evolution
of their number density in the early universe can be determined by calculating
the topological susceptibility of QCD as a function of the
temperature. Lattice QCD provides an ab initio technique to carry out such a
calculation. A full result needs two ingredients: physical quark masses and a
controlled continuum extrapolation from non-vanishing to zero lattice spacings.
We determine in the quenched framework (infinitely large quark
masses) and extrapolate its values to the continuum limit. The results are
compared with the prediction of the dilute instanton gas approximation (DIGA).
A nice agreement is found for the temperature dependence, whereas the overall
normalization of the DIGA result still differs from the non-perturbative
continuum extrapolated lattice results by a factor of order ten. We discuss the
consequences of our findings for the prediction of the amount of axion dark
matter.Comment: 9 pages, 7 figure
Fate of a recent conformal fixed point and β-function in the SU(3) BSM gauge theory with ten massless flavors
SU(3) gauge theory with fermions in the fundamental representation
serves as a theoretical testing ground for possible infrared conformal
behavior, which could play a role in BSM composite Higgs models. We use lattice
simulations to study the 10-flavor model, for which it has been claimed there
is an infrared fixed point in the gauge coupling -function. Our results
suggest the opposite conclusion, namely we find no -function fixed point
in the explored range, with qualitative agreement with the 5-loop
prediction. We comment on the inconsistency between our
findings and other studies.Comment: 7 pages, 6 figures; Proceedings for the 36th Annual International
Symposium on Lattice Field Theory, 22-28 July 2018, Michigan State
University, East Lansing, Michigan, US
Is SU(3) gauge theory with 13 massless flavors conformal?
We use lattice simulations to study SU(3) gauge theory with 13 massless
fermions in the fundamental representation. We present evidence that the theory
is conformal with a non-zero infrared fixed point in the gauge coupling. We use
a newly-developed technique to calculate the mass anomalous dimension at the
fixed point via step-scaling of the mode number, allowing us to take the
continuum limit and compare to perturbative predictions. We comment on the
relevance of these findings to the extended search for the conformal window in
the fundamental representation and in particular 12 massless flavors.Comment: 7 pages, 7 figures; Proceedings for the 36th Annual International
Symposium on Lattice Field Theory, 22-28 July 2018, Michigan State
University, East Lansing, Michigan, US
Lattice QCD as a video game
The speed, bandwidth and cost characteristics of today's PC graphics cards make them an attractive target as general purpose computational platforms. High performance can be achieved also for lattice simulations but the actual implementation can be cumbersome. This paper outlines the architecture and programming model of modern graphics cards for the lattice practitioner with the goal of exploiting these chips for Monte Carlo simulations. Sample code is also given. (c) 2007 Elsevier B.V. All rights reserved
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