10 research outputs found
Simplicial gauge theory on spacetime
We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime
simplicial meshes. The formulation is a generalization of classical lattice
gauge theory, and we prove consistency of the action in the sense of
approximation theory. In addition, we perform numerical tests of convergence
towards exact continuum results for several choices of gauge fields in pure
gauge theory.Comment: 18 pages, 2 figure
Phases of one dimensional large N gauge theory in a 1/D expansion
We consider large N Yang Mills theory with D adjoint scalar fields in d
dimensions for d=0 or 1. We show the existence of a non-trivial saddle point of
the functional integral at large D which is characterized by a mass gap for the
adjoint scalars. We integrate out the adjoint scalars in a 1/D expansion around
the saddle point. In case of one dimension which is regarded as a circle, this
procedure leads to an effective action for the Wilson line. We find an analogue
of the confinement/deconfinement transition which consists of a second order
phase transition from a uniform to a non-uniform eigenvalue distribution of the
Wilson line, closely followed by a Gross-Witten-Wadia transition where a gap
develops in the eigenvalue distribution. The phase transition can be regarded
as a continuation of a Gregory-Laflamme transition. Our methods involve large
values of the dimensionless 'tHooft coupling. The analysis in this paper is
quantitatively supported by earlier numerical work for D=9.Comment: 27 pages + 21 pages of Appendix; 8 figures, v2:some comments are
added in sec.4.3, minor corrections, one reference added, v3: minor
corrections, one reference added, version to be published in JHE
On the large N limit of SU(N) lattice gauge theories in five dimensions
We develop the necessary tools for computing fluctuations around a mean-field
background in the context of SU(N) lattice gauge theories in five dimensions.
In particular, expressions for the scalar observable and the Wilson Loop are
given. As an application, using these observables we compute a certain quantity
k5 that can be viewed as Coulomb's constant in five dimensions. We show that
this quantity becomes independent of N in the large N limit. Furthermore, the
numerical value of k5 we find for SU(infinity) deviates by 17% from its value
predicted by holography.Comment: Discussion adde
Dynamics and transport near quantum-critical points
The physics of non-zero temperature dynamics and transport near
quantum-critical points is discussed by a detailed study of the O(N)-symmetric,
relativistic, quantum field theory of a N-component scalar field in spatial
dimensions. A great deal of insight is gained from a simple, exact solution of
the long-time dynamics for the N=1 d=1 case: this model describes the critical
point of the Ising chain in a transverse field, and the dynamics in all the
distinct, limiting, physical regions of its finite temperature phase diagram is
obtained. The N=3, d=1 model describes insulating, gapped, spin chain
compounds: the exact, low temperature value of the spin diffusivity is
computed, and compared with NMR experiments. The N=3, d=2,3 models describe
Heisenberg antiferromagnets with collinear N\'{e}el correlations, and
experimental realizations of quantum-critical behavior in these systems are
discussed. Finally, the N=2, d=2 model describes the superfluid-insulator
transition in lattice boson systems: the frequency and temperature dependence
of the the conductivity at the quantum-critical coupling is described and
implications for experiments in two-dimensional thin films and inversion layers
are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical
properties of unconventional magnetic systems", Geilo, Norway, April 2-12,
1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be
published. 46 page
The string-junction picture of multiquark states: an update
We recall and update, both theoretically and phenomenologically, our (nearly)
forty-years-old proposal of a string-junction as a necessary complement to the
conventional classification of hadrons based just on their quark-antiquark
constituents. In that proposal single (though in general metastable) hadronic
states are associated with "irreducible" gauge-invariant operators consisting
of Wilson lines (visualized as strings of color flux tubes) that may either end
on a quark or an antiquark, or annihilate in triplets at a junction or an
anti-junction . For the junction-free sector (ordinary
mesons and glueballs) the picture is supported by large- (number of colors)
considerations as well as by a lattice strong-coupling expansion. Both imply
the famous OZI rule suppressing quark-antiquark annihilation diagrams. For
hadrons with and/or constituents the same expansions support our
proposal, including its generalization of the OZI rule to the suppression of
annihilation diagrams. Such a rule implies that hadrons with
junctions are "mesophobic" and thus unusually narrow if they are below
threshold for decaying into as many baryons as their total number of junctions
(two for a tetraquark, three for a pentaquark). Experimental support for our
claim, based on the observation that narrow multiquark states typically lie
below (well above) the relevant baryonic (mesonic) thresholds, will be
presented.Comment: 37 pages, 18 figures Some clarifications and several new references
adde