Conformal constraints for anomalous dimensions of leading twist operators

Leading-twist operators have a remarkable property that their divergence vanishes in a free theory. Recently it was suggested that this property can be used for an alternative technique to calculate anomalous dimensions of leading-twist operators and allows one to gain one order in perturbation theory so that, i.e., two-loop anomalous dimensions can be calculated from one-loop Feynman diagrams, etc. In this work we study feasibility of this program on a toy-model example of the $\varphi^3$ theory in six dimensions. Our conclusion is that this approach is valid, although it does not seem to present considerable technical simplifications as compared to the standard technique. It does provide one, however, with a very nontrivial check of the calculation as the structure of the contributions is very different.Comment: 14 pages, 6 figure

Two-loop conformal generators for leading-twist operators in QCD

QCD evolution equations in minimal subtraction schemes have a hidden symmetry: One can construct three operators that commute with the evolution kernel and form an $SL(2)$ algebra, i.e. they satisfy (exactly) the $SL(2)$ commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer $d=4-2\epsilon$ space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in $d=4-2\epsilon$ effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the $SL(2)$ commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD $\beta$-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.Comment: 36 page

Electroproduction of tensor mesons in QCD

Due to multiple possible polarizations hard exclusive production of tensor mesons by virtual photons or in heavy meson decays offers interesting possibilities to study the helicity structure of the underlying short-distance process. Motivated by the first measurement of the transition form factor $\gamma^*\gamma \to f_2(1270)$ at large momentum transfers by the BELLE collaboration we present an improved QCD analysis of this reaction in the framework of collinear factorization including contributions of twist-three quark-antiquark-gluon operators and an estimate of soft end-point corrections using light-cone sum rules. The results appear to be in a very good agreement with the data, in particular the predicted scaling behavior is reproduced in all cases.Comment: 27 pages, 5 figure

Correction exponents in the Gross–Neveu–Yukawa model at 1/N2

We calculate the critical exponents omega +/- in the d-dimensional Gross-Neveu model in 1/N expansion with 1/N-2 accuracy. These exponents are related to the slopes of the ss-functions at the critical point in the Gross-Neveu-Yukawa model. They have been computed recently to four loops accuracy. We checked that our results are in complete agreement with the results of the perturbative calculations

Crown-of-thorns sea star Acanthaster cf. solaris has tissue-characteristic microbiomes with potential roles in health and reproduction

© 2018 American Society for Microbiology. Outbreaks of coral-eating crown-of-thorns sea stars (CoTS; Acanthaster species complex) cause substantial coral loss; hence, there is considerable interest in developing prevention and control strategies. We characterized the microbiome of captive CoTS and assessed whether dysbiosis was evident in sea stars during a disease event. Most tissue types had a distinct microbiome. The exception was female gonads, in which the microbiomes were highly variable among individuals. Male gonads were dominated (> 97% of reads) by a single Mollicutes-related operational taxonomic unit (OTU). Detailed phylogenetic and microscopy analysis demonstrated the presence of a novel Spiroplasma-related bacterium in the spermatogenic layer. Body wall samples had high relative abundance (43 to 64% of reads) of spirochetes, likely corresponding to subcuticular symbionts reported from many echinoderms. Tube feet were characterized by Hyphomonadaceae (24 to 55% of reads). Pyloric cecal microbiomes had high alpha diversity, comprising many taxa commonly found in gastrointestinal systems. The order Oceanospirillales (genera Endozoicomonas and Kistimonas) was detected in all tissues. A microbiome shift occurred in diseased individuals although differences between tissue types were retained. The relative abundance of spirochetes was significantly reduced in diseased individuals. Kistimonas was present in all diseased individuals and significantly associated with diseased tube feet, but its role in disease causation is unknown. While Arcobacter was significantly associated with diseased tissues and Vibrionaceae increased in diversity, no single OTU was detected in all diseased individuals, suggesting opportunistic proliferation of these taxa in this case. This study shows that CoTS have tissuecharacteristic bacterial communities and identifies taxa that could play a role in reproduction and host health

Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Neel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy

Higher spin currents in the critical O(N) vector model at 1/N 2

We calculate the anomalous dimensions of higher spin singlet currents in the critical O(N) vector model at order 1/N-2. The results are shown to be in agreement with the four-loop perturbative computation in phi(4) theory in 4-2 epsilon dimensions. It is known that the order 1/N anomalous dimensions of higher-spin currents happen to be the same in the Gross-Neveu and the critical vector model. On the contrary, the order 1/N-2 corrections are different. The results can also be interpreted as a prediction for the two-loop computation in the dual higher-spin gravity

High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators and therefore the system remains non-commutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.Comment: 26 pages, latex2

Similarity bias in credit decisions for entrepreneurs on the brink of bankruptcy

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