Quantum Criticality and Yang-Mills Gauge Theory

We present a family of nonrelativistic Yang-Mills gauge theories in D+1 dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2. The ground state wavefunction is intimately related to the partition function of relativistic Yang-Mills in D dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4+1. The theories can be deformed in the infrared by a relevant operator that restores Poincare invariance as an accidental symmetry. In the large-N limit, our nonrelativistic gauge theories can be expected to have weakly curved gravity duals.Comment: 10 page

QCD_4 From a Five-Dimensional Point of View

We propose a 5-dimensional definition for the physical 4D-Yang-Mills theory. The fifth dimension corresponds to the Monte-Carlo time of numerical simulations of QCD_4. The 5-dimensional theory is a well-defined topological quantum field theory that can be renormalized at any given finite order of perturbation theory. The relation to non-perturbative physics is obtained by expressing the theory on a lattice, a la Wilson. The new fields that must be introduced in the context of a topological Yang-Mills theory have a simple lattice expression. We present a 5-dimensional critical limit for physical correlation functions and for dynamical auto-correlations, which allows new Monte-Carlo algorithm based on the time-step in lattice units given by \e = g_0^{-13/11} in pure gluodynamics. The gauge-fixing in five dimensions is such that no Gribov ambiguity occurs. The weight is strictly positive, because all ghost fields have parabolic propagators and yield trivial determinants. We indicate how our 5-dimensional description of the Yang-Mills theory may be extended to fermions.Comment: 45 page

Non-renormalizability of the HMC algorithm

In lattice field theory, renormalizable simulation algorithms are attractive, because their scaling behaviour as a function of the lattice spacing is predictable. Algorithms implementing the Langevin equation, for example, are known to be renormalizable if the simulated theory is. In this paper we show that the situation is different in the case of the molecular-dynamics evolution on which the HMC algorithm is based. More precisely, studying the phi^4 theory, we find that the hyperbolic character of the molecular-dynamics equations leads to non-local (and thus non-removable) ultraviolet singularities already at one-loop order of perturbation theory.Comment: Plain TeX source, 23 pages, 3 figures included; v2: typos corrected, agrees with published versio

Time-independant stochastic quantization, DS equations, and infrared critical exponents in QCD

We derive the equations of time-independent stochastic quantization, without reference to an unphysical 5th time, from the principle of gauge equivalence. It asserts that probability distributions $P$ that give the same expectation values for gauge-invariant observables $= \int dA W P$ are physically indistiguishable. This method escapes the Gribov critique. We derive an exact system of equations that closely resembles the Dyson-Schwinger equations of Faddeev-Popov theory, which we then solve non-perturbatively for the critical exponents that characterize the asymptotic form at $k \approx 0$ of the tranverse and longitudinal parts of the gluon propagator in Landau gauge, D^T \sim (k^2)^{-1-\a_T} and D^L \sim a (k^2)^{-1-\a_L}, and obtain \a_T = - 2\a_L \approx - 1.043 (short range), and \a_L \approx 0.521, (long range). Although the longitudinal part vanishes with the gauge parameter $a$ in the Landau gauge limit, $a \to 0$, there are vertices of order $a^{-1}$, so the longitudinal part of the gluon propagator contributes in internal lines, replacing the ghost that occurs in Faddeev-Popov theory. We compare our results with the corresponding results in Faddeev-Popov theory.Comment: 50 pages, 2 figure

Polycomb Repressive Complex 2 Controls the Embryo-to-Seedling Phase Transition

Polycomb repressive complex 2 (PRC2) is a key regulator of epigenetic states catalyzing histone H3 lysine 27 trimethylation (H3K27me3), a repressive chromatin mark. PRC2 composition is conserved from humans to plants, but the function of PRC2 during the early stage of plant life is unclear beyond the fact that it is required for the development of endosperm, a nutritive tissue that supports embryo growth. Circumventing the requirement of PRC2 in endosperm allowed us to generate viable homozygous null mutants for FERTILIZATION INDEPENDENT ENDOSPERM (FIE), which is the single Arabidopsis homolog of Extra Sex Combs, an indispensable component of Drosophila and mammalian PRC2. Here we show that H3K27me3 deposition is abolished genome-wide in fie mutants demonstrating the essential function of PRC2 in placing this mark in plants as in animals. In contrast to animals, we find that PRC2 function is not required for initial body plan formation in Arabidopsis. Rather, our results show that fie mutant seeds exhibit enhanced dormancy and germination defects, indicating a deficiency in terminating the embryonic phase. After germination, fie mutant seedlings switch to generative development that is not sustained, giving rise to neoplastic, callus-like structures. Further genome-wide studies showed that only a fraction of PRC2 targets are transcriptionally activated in fie seedlings and that this activation is accompanied in only a few cases with deposition of H3K4me3, a mark associated with gene activity and considered to act antagonistically to H3K27me3. Up-regulated PRC2 target genes were found to act at different hierarchical levels from transcriptional master regulators to a wide range of downstream targets. Collectively, our findings demonstrate that PRC2-mediated regulation represents a robust system controlling developmental phase transitions, not only from vegetative phase to flowering but also especially from embryonic phase to the seedling stage