14,811 research outputs found
Breakdown of large-N quenched reduction in SU(N) lattice gauge theories
We study the validity of the large-N equivalence between four-dimensional
SU(N) lattice gauge theory and its momentum quenched version--the Quenched
Eguchi-Kawai (QEK) model. We find that the assumptions needed for the proofs of
equivalence do not automatically follow from the quenching prescription. We use
weak-coupling arguments to show that large-N equivalence is in fact likely to
break down in the QEK model, and that this is due to dynamically generated
correlations between different Euclidean components of the gauge fields. We
then use Monte-Carlo simulations at intermediate couplings with 20 <= N <= 200
to provide strong evidence for the presence of these correlations and for the
consequent breakdown of reduction. This evidence includes a large discrepancy
between the transition coupling of the "bulk" transition in lattice gauge
theories and the coupling at which the QEK model goes through a strongly
first-order transition. To accurately measure this discrepancy we adapt the
recently introduced Wang-Landau algorithm to gauge theories.Comment: 51 pages, 16 figures, Published verion. Historical inaccuracies in
the review of the quenched Eguchi-Kawai model are corrected, discussion on
reduction at strong-coupling added, references updated, typos corrected. No
changes to results or conclusion
Infinite number of MSSMs from heterotic line bundles?
We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau
manifolds with line bundle gauge backgrounds. Infinite sets of models that
satisfy the Bianchi identities and flux quantization conditions can be
constructed by letting their background flux quanta grow without bound. Even
though we do not have a general proof, we find that all examples are at the
boundary of the theory's validity: the Donaldson-Uhlenbeck-Yau equations, which
can be thought of as vanishing D-term conditions, cannot be satisfied inside
the Kaehler cone unless a growing number of scalar Vacuum Expectation Values
(VEVs) is switched on. As they are charged under various line bundles
simultaneously, the gauge background gets deformed by these VEVs to a
non-Abelian bundle. In general, our physical expectation is that such infinite
sets of models should be impossible, since they never seem to occur in exact
CFT constructions.Comment: LaTeX, 8 pages, 4 tables, some references and comments adde
On the freezing of variables in random constraint satisfaction problems
The set of solutions of random constraint satisfaction problems (zero energy
groundstates of mean-field diluted spin glasses) undergoes several structural
phase transitions as the amount of constraints is increased. This set first
breaks down into a large number of well separated clusters. At the freezing
transition, which is in general distinct from the clustering one, some
variables (spins) take the same value in all solutions of a given cluster. In
this paper we study the critical behavior around the freezing transition, which
appears in the unfrozen phase as the divergence of the sizes of the
rearrangements induced in response to the modification of a variable. The
formalism is developed on generic constraint satisfaction problems and applied
in particular to the random satisfiability of boolean formulas and to the
coloring of random graphs. The computation is first performed in random tree
ensembles, for which we underline a connection with percolation models and with
the reconstruction problem of information theory. The validity of these results
for the original random ensembles is then discussed in the framework of the
cavity method.Comment: 32 pages, 7 figure
Numerical simulation evidence of spectrum rearrangement in impure graphene
By means of numerical simulation we confirm that in graphene with point
defects a quasigap opens in the vicinity of the resonance state with increasing
impurity concentration. We prove that states inside this quasigap cannot longer
be described by a wavevector and are strongly localized. We visualize states
corresponding to the density of states maxima within the quasigap and show that
they are yielded by impurity pair clusters
Ewald summation on a helix : a route to self-consistent charge density-functional based tight-binding objective molecular dynamics
We explore the generalization to the helical case of the classical Ewald method, the harbinger of all modern self-consistent treatments of waves in crystals, including ab initio electronic structure methods. Ewald-like formulas that do not rely on a unit cell with translational symmetry prove to be numerically tractable and able to provide the crucial component needed for coupling objective molecular dynamics with the self-consistent charge density-functional based tight-binding treatment of the inter-atomic interactions. The robustness of the method in addressing complex hetero-nuclear nano- and bio-systems is demonstrated with illustrative simulations on a helical boron nitride nanotube, a screw dislocated zinc oxide nanowire, and an ideal DNA molecule
- âŠ