Orbital Compass Model as an Itinerant Electron System

Two-dimensional orbital compass model is studied as an interacting itinerant electron model. A Hubbard-type tight-binding model, from which the orbital compass model is derived in the strong coupling limit, is identified. This model is analyzed by the random-phase approximation (RPA) and the self-consistent RPA methods from the weak coupling. Anisotropy for the orbital fluctuation in the momentum space is qualitatively changed by the on-site Coulomb interaction. This result is explained by the fact that the dominant fluctuation is changed from the intra-band nesting to the inter-band one by increasing the interaction.Comment: 7 pages, 8 figure

Empirical Determination of Threshold Partial Wave Amplitudes in pp→ppωp p \to p p \omega

Using the model independent irreducible tensor approach to $\omega$ production in $pp$ collisions, we show theoretically that, it is advantageous to measure experimentally the polarization of $\omega$, in addition to the proposed experimental study employing a polarized beam and a polarized target.Comment: 6 pages, 1 Table, Latex-2

The aa-theorem and the Asymptotics of 4D Quantum Field Theory

We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that if the IR (UV) asymptotics is described by perturbation theory, all beta functions must vanish faster than $(1/|\ln\mu|)^{1/2}$ as $\mu \to 0$ ($\mu \to \infty$). This implies that the only possible asymptotics within perturbation theory is conformal field theory. In particular, it rules out perturbative theories with scale but not conformal invariance, which are equivalent to theories with renormalization group pseudocycles. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise.Comment: 41 pages, 2 figures. v2: Arguments clarified, some side comments corrected, connection to previous work by Jack and Osborn described, conclusions unaffecte

Observables and Correlators in Nonrelativistic ABJM Theory

Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed N=6 Chern-Simons theory. Holographic string theory dual to the theory is not known yet. To understand features candidate gravity dual might exhibit, we examine local and nonlocal physical observables and their correlations in the non-relativistic ABJM theory. We show that gauge invariant local observables correspond to zero-norm states and that correlation functions among them are trivial. We also show that a particular class of nonlocal observables, Wilson loops, are topological in the sense that their correlation functions coincide with those of pure Chern-Simons theory. We argue that the theory is nevertheless physical and illustrate several physical observables whose correlation functions are nontrivial. We also study quantum aspects. We show that Chern-Simons level is finitely renormalized and that dilatation operator acting on spin chain is trivial at planar limit. These results all point to string scale geometry of gravity dual and to intriguing topological and tensionless nature of dual string defined on it.Comment: 1+30 pages, no figure, v2. typos fixed and references adde

Limit Cycles in Four Dimensions

We present an example of a limit cycle, i.e., a recurrent flow-line of the beta-function vector field, in a unitary four-dimensional gauge theory. We thus prove that beta functions of four-dimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory with a three-loop calculation which we describe in detail.Comment: 12 pages, 1 figure. Significant revision of the interpretation of our result. Improved description of three-loop calculatio

Continuum Annulus Amplitude from the Two-Matrix Model

An explicit expression for continuum annulus amplitudes having boundary lengths $\ell_{1}$ and $\ell_{2}$ is obtained from the two-matrix model for the case of the unitary series; $(p,q) = (m + 1, m)$. In the limit of vanishing cosmological constant, we find an integral representation of these amplitudes which is reproduced, for the cases of the $m = 2~(c=0)$ and the $m \rightarrow \infty~(c=1)$, by a continuum approach consisting of quantum mechanics of loops and a matter system integrated over the modular parameter of the annulus. We comment on a possible relation to the unconventional branch of the Liouville gravity.Comment: 9 pages, OU-HET 190, revised version. A part of the conclusions has been corrected. A new result on integral representation of the annulus amplitudes has been adde

RNA and epigenetic silencing: Insight from fission yeast

Post-translational modifications of histones are critical not only for local regulation of gene expression, but also for higher-order structure of the chromosome and genome organization in general. These modifications enable a preset state to be maintained over subsequent generations and thus provide an epigenetic level of regulation. Heterochromatic regions of the genome are epigenetically regulated to maintain a "silent state" and protein coding genes inserted into these regions are subject to the same epigenetic silencing. The fission yeast Schizosaccharomyces pombe has well characterized regions of heterochromatin and has proven to be a powerful model for elucidation of epigenetic silencing mechanisms. Research in S. pombe led to the breakthrough discovery that epigenetic silencing is not solely a chromatin-driven transcriptional repression and that RNA interference of nascent transcripts can guide epigenetic silencing and associated histone modifications. Over the last 10years, an eloquent integration of genetic and biochemical studies have greatly propelled our understanding of major players and effector complexes for regulation of RNAi-mediated epigenetic silencing in S. pombe. Here, we review recent research related to regulation of the epigenetic state in S. pombe heterochromatin, focusing specifically on the mechanisms by which transcription and RNA processing interact with the chromatin modification machinery to maintain the epigenetically silent state

Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly

From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four-dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomophic theory of gravity could be inconsistent with a theorem of the dual unitary quantum field theory.Comment: 18 pages, v2: reference added, v3: comments on more recent literature added in response to referee's reques

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Enhanced Supersymmetry of Nonrelativistic ABJM Theory

We study the supersymmetry enhancement of nonrelativistic limits of the ABJM theory for Chern-Simons level $k=1,2$. The special attention is paid to the nonrelativistic limit (known as `PAAP' case) containing both particles and antiparticles. Using supersymmetry transformations generated by the monopole operators, we find additional 2 kinematical, 2 dynamical, and 2 conformal supercharges for this case. Combining with the original 8 kinematical supercharges, the total number of supercharges becomes maximal: 14 supercharges, like in the well-known PPPP limit. We obtain the corresponding super Schr\"odinger algebra which appears to be isomorphic to the one of the PPPP case. We also discuss the role of monopole operators in supersymmetry enhancement and partial breaking of supersymmetry in nonrelativistic limit of the ABJM theory.Comment: 22 pages, references added, version to appear in JHE