47 research outputs found
String and M-theory: answering the critics
Using as a springboard a three-way debate between theoretical physicist Lee
Smolin, philosopher of science Nancy Cartwright and myself, I address in
layman's terms the issues of why we need a unified theory of the fundamental
interactions and why, in my opinion, string and M-theory currently offer the
best hope. The focus will be on responding more generally to the various
criticisms. I also describe the diverse application of string/M-theory
techniques to other branches of physics and mathematics which render the whole
enterprise worthwhile whether or not "a theory of everything" is forthcoming.Comment: Update on EPSRC. (Contribution to the Special Issue of Foundations of
Physics: "Forty Years Of String Theory: Reflecting On the Foundations",
edited by Gerard 't Hooft, Erik Verlinde, Dennis Dieks and Sebastian de Haro.
22 pages latex
Classical Sphaleron Rate on Fine Lattices
We measure the sphaleron rate for hot, classical Yang-Mills theory on the
lattice, in order to study its dependence on lattice spacing. By using a
topological definition of Chern-Simons number and going to extremely fine
lattices (up to beta=32, or lattice spacing a = 1 / (8 g^2 T)) we demonstrate
nontrivial scaling. The topological susceptibility, converted to physical
units, falls with lattice spacing on fine lattices in a way which is consistent
with linear dependence on (the Arnold-Son-Yaffe scaling relation) and
strongly disfavors a nonzero continuum limit. We also explain some unusual
behavior of the rate in small volumes, reported by Ambjorn and Krasnitz.Comment: 14 pages, includes 5 figure
Chern-Simons Number Diffusion and Hard Thermal Loops on the Lattice
We develop a discrete lattice implementation of the hard thermal loop
effective action by the method of added auxiliary fields. We use the resulting
model to measure the sphaleron rate (topological susceptibility) of Yang-Mills
theory at weak coupling. Our results give parametric behavior in accord with
the arguments of Arnold, Son, and Yaffe, and are in quantitative agreement with
the results of Moore, Hu, and Muller.Comment: 43 pages, 6 figure
Continuum Gauge Fields from Lattice Gauge Fields
On the lattice some of the salient features of pure gauge theories and of
gauge theories with fermions in complex representations of the gauge group seem
to be lost. These features can be recovered by considering part of the theory
in the continuum. The prerequisite for that is the construction of continuum
gauge fields from lattice gauge fields. Such a construction, which is gauge
covariant and complies with geometrical constructions of the topological charge
on the lattice, is given in this paper. The procedure is explicitly carried out
in the theory in two dimensions, where it leads to simple results.Comment: 16 pages, HLRZ 92-3
The Sphaleron Rate in SU(N) Gauge Theory
The sphaleron rate is defined as the diffusion constant for topological
number NCS = int g^2 F Fdual/32 pi^2. It establishes the rate of equilibration
of axial light quark number in QCD and is of interest both in electroweak
baryogenesis and possibly in heavy ion collisions. We calculate the
weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most
sensible extrapolation towards intermediate coupling which we can. We also
study the behavior of the sphaleron rate at weak coupling at large Nc.Comment: 18 pages with 3 figure