Local Couplings and Sl(2,R) Invariance for Gauge Theories at One Loop

The response of the one loop effective action for a gauge theory with local couplings $g(x),\theta(x)$ under a local Weyl rescaling of the background metric is calculated. Apart from terms which may be removed by local contributions to the effective action the result is compatible with $Sl(2,R)$ symmetry acting on $g,\theta$. Two loop effects are also discussed.Comment: 10 pages, uses harvma

Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the ε\varepsilon Expansion

The tensorial equations for non trivial fully interacting fixed points at lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and $3-\varepsilon$ dimensions are analysed for $N$-component fields and corresponding multi-index couplings $\lambda$ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For $N=5,6,7$ in the four-index case large numbers of irrational fixed points are found numerically where $||\lambda ||^2$ is close to the bound found by Rychkov and Stergiou in arXiv:1810.10541. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For $N \geqslant 6$ the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for $N=5$.Comment: 50 pages, 6 figures. v2: 53 pages, 6 figures; Expanded discussion of N=4 case including splitting of fixed point at order $\varepsilon^2$; v4: Minor corrections and addition

Modified Weak Energy Condition for the Energy Momentum Tensor in Quantum Field Theory

The weak energy condition is known to fail in general when applied to expectation values of the the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states |\psi \r for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on |\psi \r is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on |\psi \r are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories.Comment: 27 pages, 1 figure, uses harvmac, epsf and boldmath (included). Change of title and some text changes, form to be publishe

N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory

The implications of N=1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and connected with the operator product expansion. The general formulae are specialised to cases involving a scalar superfield L, which contains global symmetry currents, and the supercurrent, which contains the energy momentum tensor, and the consequences of superconformal Ward identities analysed. The three point function of L is shown to have unique completely antisymmetric or symmetric forms. In the latter case the superspace version of the axial anomaly equation is obtained. The three point function for the supercurrent is shown to have two linearly independent forms. A linear combination of the associated coefficients for the general expression is shown to be related to the scale of the supercurrent two point function through Ward identities. The coefficients are given for the two free field superconformal theories and are also connected with the parameters present in the supercurrent anomaly for supergravity backgrounds. Superconformal invariants, which are possible even in three point functions, are discussed.Comment: 53 pages, uses harvmac, revised version includes further corrections and minor additions, version to be publishe

The host stars of Kepler's habitable exoplanets : superflares, rotation and activity

We embark on a detailed study of the light curves of Kepler's most Earth-like exoplanet host stars using the full length of Kepler data. We derive rotation periods, photometric activity indices, flaring energies, mass-loss rates, gyrochronological ages, X-ray luminosities and consider implications for the planetary magnetospheres and habitability. Furthermore, we present the detection of superflares in the light curve of Kepler-438, the exoplanet with the highest Earth Similarity Index to date. Kepler-438b orbits at a distance of 0.166 au to its host star, and hence may be susceptible to atmospheric stripping. Our sample is taken from the Habitable Exoplanet Catalogue, and consists of the stars Kepler-22, Kepler-61, Kepler-62, Kepler-174, Kepler-186, Kepler-283, Kepler-296, Kepler-298, Kepler-438, Kepler-440, Kepler-442, Kepler-443 and KOI-4427, between them hosting 15 of the most habitable transiting planets known to date from Kepler

Absorbent particles, especially catamenials, having improved fluid directionality, comfort and fit

Absorbent articles, especially sanitary napkins, contain fibers with intra-fiber capillary channels. In-use, the capillary channel fibers direct menses to a storage layer, thereby minimizing product failure and staining of undergarments. The capillary channel fibers can protrude into, or through, a topsheet to provide very aggressive transport of vaginal discharges