2,074 research outputs found
Constrained Hybrid Monte Carlo algorithms for gauge-Higgs models
We develop Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian
systems of gauge- Higgs models and introduce a new observable for the
constraint effective Higgs potential. We use an extension of the so-called
Rattle algorithm to general Hamiltonians for constrained systems, which we
adapt to the 4D Abelian-Higgs model and the 5D SU(2) gauge theory on the torus
and on the orbifold. The derivative of the potential is measured via the
expectation value of the Lagrange multiplier for the constraint condition and
allows a much more precise determination of the effective potential than
conventional histogram methods. With the new method, we can access the
potential over the full domain of the Higgs variable, while the histogram
method is restricted to a short region around the expectation value of the
Higgs field in unconstrained simulations, and the statistical precision does
not deteriorate when the volume is increased. We further verify our results by
comparing to the one-loop Higgs potential of the 4D Abelian-Higgs model in
unitary gauge and find good agreement. To our knowledge, this is the first time
this problem has been addressed for theories with gauge fields. The algorithm
can also be used in four dimensions to study finite temperature and density
transitions via effective Polyakov loop actions.Comment: added comparison to one-loop potential in section 3.3, improved text;
version accepted for publication in Computer Physics Communication
Vistas in numerical relativity
Upcoming gravitational wave-experiments promise a window for discovering new
physics in astronomy. Detection sensitivity of the broadband laser
interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with
accurate wave-form templates. Where analytic methods break down, we have to
resort to numerical relativity, often in Hamiltonian or various hyperbolic
formulations. Well-posed numerical relativity requires consistency with the
elliptic constraints of energy and momentum conservation. We explore this using
a choice of gauge in the future and a dynamical gauge in the past. Applied to a
polarized Gowdy wave, this enables solving {\em all} ten vacuum Einstein
equations. Evolution of the Schwarzschild metric in 3+1 and, more generally,
sufficient conditions for well-posed numerical relativity continue to be open
challenges.Comment: invited talk, Asian Pacific CTP Winter School on black hole
astrophysics, Pohang, Kore
Gribov Problem for Gauge Theories: a Pedagogical Introduction
The functional-integral quantization of non-Abelian gauge theories is
affected by the Gribov problem at non-perturbative level: the requirement of
preserving the supplementary conditions under gauge transformations leads to a
non-linear differential equation, and the various solutions of such a
non-linear equation represent different gauge configurations known as Gribov
copies. Their occurrence (lack of global cross-sections from the point of view
of differential geometry) is called Gribov ambiguity, and is here presented
within the framework of a global approach to quantum field theory. We first
give a simple (standard) example for the SU(2) group and spherically symmetric
potentials, then we discuss this phenomenon in general relativity, and recent
developments, including lattice calculations.Comment: 24 pages, Revtex 4. In the revised version, a statement has been
amended on page 11, and References 14, 16 and 27 have been improve
Numerical Approaches to Spacetime Singularities
This Living Review updates a previous version which its itself an update of a
review article. Numerical exploration of the properties of singularities could,
in principle, yield detailed understanding of their nature in physically
realistic cases. Examples of numerical investigations into the formation of
naked singularities, critical behavior in collapse, passage through the Cauchy
horizon, chaos of the Mixmaster singularity, and singularities in spatially
inhomogeneous cosmologies are discussed.Comment: 51 pages, 6 figures may be found in online version: Living Rev.
Relativity 2002-1 at www.livingreviews.or
A simplicial gauge theory
We provide an action for gauge theories discretized on simplicial meshes,
inspired by finite element methods. The action is discretely gauge invariant
and we give a proof of consistency. A discrete Noether's theorem that can be
applied to our setting, is also proved.Comment: 24 pages. v2: New version includes a longer introduction and a
discrete Noether's theorem. v3: Section 4 on Noether's theorem has been
expanded with Proposition 8, section 2 has been expanded with a paragraph on
standard LGT. v4: Thorough revision with new introduction and more background
materia
Lecture Notes on Turbulent Instability of Anti-de Sitter Spacetime
In these lecture notes we discuss recently conjectured instability of anti-de
Sitter space, resulting in gravitational collapse of a large class of
arbitrarily small initial perturbations. We uncover the technical details used
in the numerical study of spherically symmetric Einstein-massless scalar field
system with negative cosmological constant that led to the conjectured
instability.Comment: Lecture notes from the NRHEP spring school held at IST-Lisbon, March
2013. To be published by IJMPA (V. Cardoso, L. Gualtieri, C. Herdeiro and U.
Sperhake, Eds., 2013); v2: sec. 6 and acknowledgments added, matches
published versio
A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
This article studies a numerical relativity approach to the initial value
problem in Anti-de Sitter spacetime relevant for dual non-equilibrium evolution
of strongly coupled non-Abelian plasma undergoing Bjorken expansion. In order
to use initial conditions for the metric obtained in arXiv:0906.4423 we
introduce new, ADM formalism-based scheme for numerical integration of
Einstein's equations with negative cosmological constant. The key novel element
of this approach is the choice of lapse function vanishing at fixed radial
position, enabling, if needed, efficient horizon excision. Various physical
aspects of the gauge theory thermalization process in this setup have been
outlined in our companion article arXiv:1103.3452. In this work we focus on the
gravitational side of the problem and present full technical details of our
setup. We discuss in particular the ADM formalism, the explicit form of initial
states, the boundary conditions for the metric on the inner and outer edges of
the simulation domain, the relation between boundary and bulk notions of time,
the procedure to extract the gauge theory energy-momentum tensor and
non-equilibrium apparent horizon entropy, as well as the choice of point for
freezing the lapse. Finally, we comment on various features of the initial
profiles we consider.Comment: 25 pages, 9 figures, 1 table; see also the companion article
arXiv:1103.3452; v2: typos fixed; v3: references added and updated, publishe
Non-Abelian Dual Superconductor Picture for Quark Confinement
We give a theoretical framework for defining and extracting non-Abelian
magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study
quark confinement. Then we give numerical evidences that the non-Abelian
magnetic monopole defined in this way gives a dominant contribution to
confinement of fundamental quarks in SU(3) Yang-Mills theory, which is in sharp
contrast to the SU(2) case in which Abelian magnetic monopoles play the
dominant role for quark confinement.Comment: 9 pages, 3 figures (4 ps files); The paper was extensively revised,
focusing especially on the lattice par
Numerical and analytical methods for asymptotically flat spacetimes
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating asymptotically flat spacetimes of infinite extent with finite computational resources. Two different approaches are considered. The first approach is the standard one and is based on evolution on Cauchy hypersurfaces with artificial timelike boundary. The well posedness of a set of constraint-preserving boundary conditions for the Einstein equations in generalised harmonic gauge is analysed, their numerical performance is compared with various alternate methods, and improved absorbing boundary conditions are constructed and implemented. In the second approach, one solves the Einstein equations on hyperboloidal (asymptotically characteristic) hypersurfaces. These are conformally compactified towards future null infinity, where gravitational radiation is defined in an unambiguous way. We show how the formally singular terms arising in a reduction of the equations can be evaluated at future null infinity, present stable numerical evolutions of vacuum axisymmetric black hole spacetimes and study late-time power-law tails of matter fields in spherical symmetry
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