High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrich splitting, the WENO reconstruction, the physical-constraints-preserving flux limiter, and the high-order strong stability preserving time discretization. They are extensions of the positivity-preserving finite difference WENO schemes for the non-relativistic Euler equations. However, developing physical-constraints-preserving methods for the RHD system becomes much more difficult than the non-relativistic case because of the strongly coupling between the RHD equations, no explicit expressions of the primitive variables and the flux vectors, in terms of the conservative vector, and one more physical constraint for the fluid velocity in addition to the positivity of the rest-mass density and the pressure. The key is to prove the convexity and other properties of the admissible state set and discover a concave function with respect to the conservative vector replacing the pressure which is an important ingredient to enforce the positivity-preserving property for the non-relativistic case. Several one- and two-dimensional numerical examples are used to demonstrate accuracy, robustness, and effectiveness of the proposed physical-constraints-preserving schemes in solving RHD problems with large Lorentz factor, or strong discontinuities, or low rest-mass density or pressure etc.Comment: 39 pages, 13 figure

Brief comments on Jackiw-Teitelboim gravity coupled to Liouville theory

Jackiw-Teitelboim gravity with non-vanishing cosmological constant coupled to Liouville theory is considered as a non-critical string on $d$ dimensional flat spacetime. It is discussed how the presence of cosmological constant yields additional constraints on the parameter space of the theory, even when the conformal anomaly is independent of the cosmological constant. Such constraints agree with the necessary conditions for the tachyon field to be a primary --prelogarithmic-- operator of the worldsheet conformal field theory. Thus, the linearized tachyon field equation allows to impose the diagonal condition for the interaction term. We analyze the neutralization of the Liouville mode induced by the coupling to the Jackiw-Teitelboim Lagrangian. The free field prescription leads to obtain explicit expressions for three-point correlation functions for the case of vanishing cosmological constant in terms of a product of Shapiro-Virasoro integrals. This is a consequence of the mentioned neutralization effect.Comment: 14 pages, no figures. v2 References added. To be published in Classical and Quantum Gravity. v3 typos correcte

Brane Boxes: Bending and Beta Functions

We study the type IIB brane box configurations recently introduced by Hanany and Zaffaroni. We show that even at finite string coupling, one can construct smooth configurations of branes with fairly arbitrary gauge and flavor structure. Limiting our attention to the better understood case where NS-branes do not intersect over a four dimensional surface gives some restrictions on the theories, but still permits many examples, both anomalous and non-anomalous. We give several explicit examples of such configurations and discuss what constraints can be imposed on brane-box theories from bending considerations. We also discuss the relation between brane bending and beta-functions for brane-box configurations.Comment: latex, 18 pages, 8 figure

Tensorial conservation law for nematic polymers

We derive the "conservation law" for nematic polymers in tensorial form valid for quadrupolar orientational order in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the coupling between the orientational field deformations and the density variations for polar and quadrupolar order, we find that respective order parameters satisfy fundamentally distinct constraints. Being necessarily scalar in its form, the tensorial conservation law is obtained straightforwardly from the gradients of the polymer nematic tensor field and connects the spatial variation of this tensor field with density variations. We analyze the differences between the polar and the tensorial forms of the conservation law, present some explicit orientational fields that satisfy this new constraint and discuss the role of singular "hairpins", which do not affect local quadrupolar order of polymer nematics, but nevertheless influence its gradients.Comment: 10 pages, 6 figure

Gravitinos from Heavy Scalar Decay

Cosmological issues of the gravitino production by the decay of a heavy scalar field $X$ are examined, assuming that the damped coherent oscillation of the scalar once dominates the energy of the universe. The coupling of the scalar field to a gravitino pair is estimated both in spontaneous and explicit supersymmetry breaking scenarios, with the result that it is proportional to the vacuum expectation value of the scalar field in general. Cosmological constraints depend on whether the gravitino is stable or not, and we study each case separately. For the unstable gravitino with $M_{3/2} \sim$ 100GeV--10TeV, we obtain not only the upper bound, but also the lower bound on the reheating temperature after the $X$ decay, in order to retain the success of the big-bang nucleosynthesis. It is also shown that it severely constrains the decay rate into the gravitino pair. For the stable gravitino, similar but less stringent bounds are obtained to escape the overclosure by the gravitinos produced at the $X$ decay. The requirement that the free-streaming effect of such gravitinos should not suppress the cosmic structures at small scales eliminates some regions in the parameter space, but still leaves a new window of the gravitino warm dark matter. Implications of these results to inflation models are discussed. In particular, it is shown that modular inflation will face serious cosmological difficulty when the gravitino is unstable, whereas it can escape the constraints for the stable gravitino. A similar argument offers a solution to the cosmological moduli problem, in which the moduli is relatively heavy while the gravitino is light.Comment: 14 pages, 8 figure

Planck Scale Symmetry Breaking and Majoron Physics

Majoron models provide neutrino masses via the spontaneous breaking of a global $U(1)$ symmetry. However, it may be argued that all global symmetries will be explicitly violated by gravitational effects. We show that it is possible to preserve most of the usual features of majoron models by invoking $U(1)_{B-L}$ to be a gauge symmetry and adding a second singlet scalar field. The majoron gets a small model dependent mass. The couplings of majorons to neutrinos may be of ordinary strength or may be made arbitrarily weak. We discuss the cosmological and astrophysical consequences of majoron models in the context of a model dependent majoron mass and neutrino coupling. For an appropriate choice of parameters majorons can play the role of dark matter.Comment: 30 pages, UM-TH-92-3

The superspace geometry of gravitational Chern-Simons forms and their couplings to linear multiplets : a review

The superspace geometry of Chern-Simons forms is shown to be closely related to that of the 3-form multiplet. This observation allows to simplify considerably the geometric structure of supersymmetric Chern-Simons forms and their coupling to linear multiplets. The analysis is carried through in U_K(1) superspace, relevant at the same time for supergravity-matter couplings and for chirally extended supergravity.Comment: 82 pages, LateX2