Hadron-quark continuity induced by the axial anomaly in dense QCD

We investigate the interplay between the chiral and diquark condensates on the basis of the Ginzburg-Landau potential with QCD symmetry. We demonstrate that the axial anomaly drives a new critical point at low temperature in the QCD phase diagram and leads to a smooth crossover between the hadronic and color superconducting phases.Comment: 4 pages, 5 figures, to appear in the Proceedings of Quark Matter 2006 held in Shangha

Color Superconductivity from Supersymmetry

A supersymmetric composite model of color superconductivity is proposed. Quarks and diquarks are dynamically generated as composite fields by a newly introduced strong gauge dynamics. It is shown that the condensation of the scalar component of the diquark supermultiplet occurs when the chemical potential becomes larger than some critical value. We believe that the model well captures aspects of the diquark condensate behavior and helps our understanding of the diquark dynamics in real QCD. The results obtained here might be useful when we consider a theory composed of quarks and diquarks.Comment: 4 pages, 2 figures, An error in Eq.(10) correcte

Concurrent π\pi-vector fields and energy beta-change

The present paper deals with an \emph{intrinsic} investigation of the notion of a concurrent $\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\beta$-change, namely the energy $\beta$-change ($\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \ B:=g(\bar{\zeta},\bar{\eta})$;$\bar{\zeta} $being a concurrent$\pi$-vector field), is established. The relation between the two Barthel connections$\Gamma$and$\widetilde{\Gamma}$, corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy$\beta$-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.Comment: 27 pages, LaTex file, Some typographical errors corrected, Some formulas simpifie

Closed conformal Killing-Yano tensor and geodesic integrability

Assuming the existence of a single rank-2 closed conformal Killing-Yano tensor with a certain symmetry we show that there exist mutually commuting rank-2 Killing tensors and Killing vectors. We also discuss the condition of separation of variables for the geodesic Hamilton-Jacobi equations.Comment: 17 pages, no figure, LaTe

Conformal Yano-Killing tensor for the Kerr metric and conserved quantities

Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano--Killing tensor. The relation between spin-2 fields and solutions to the Maxwell equations is used in the construction of a new conserved quantity which is quadratic in terms of the Weyl tensor. The formula obtained is similar to the functional obtained from the Bel--Robinson tensor and is examined in Kerr spacetime. A new interpretation of the conserved quantity obtained is proposed.Comment: 29 page

The origin of short-lived radionuclides and the astrophysical environment of solar system formation

Based on early solar system abundances of short-lived radionuclides (SRs), such as $^{26}$Al (T$_{1/2} = 0.74$ Myr) and $^{60}$Fe (T$_{1/2} = 1.5$ Myr), it is often asserted that the Sun was born in a large stellar cluster, where a massive star contaminated the protoplanetary disk with freshly nucleosynthesized isotopes from its supernova (SN) explosion. To account for the inferred initial solar system abundances of short-lived radionuclides, this supernova had to be close ($\sim$ 0.3 pc) to the young ($\leqslant$ 1 Myr) protoplanetary disk. Here we show that massive star evolution timescales are too long, compared to typical timescales of star formation in embedded clusters, for them to explode as supernovae within the lifetimes of nearby disks. This is especially true in an Orion Nebular Cluster (ONC)-type of setting, where the most massive star will explode as a supernova $\sim$ 5 Myr after the onset of star formation, when nearby disks will have already suffered substantial photoevaporation and/or formed large planetesimals. We quantify the probability for {\it any} protoplanetary disk to receive SRs from a nearby supernova at the level observed in the early solar system. Key constraints on our estimate are: (1) SRs have to be injected into a newly formed ($\leqslant$ 1 Myr) disk, (2) the disk has to survive UV photoevaporation, and (3) the protoplanetary disk must be situated in an enrichment zone permitting SR injection at the solar system level without disk disruption. The probability of protoplanetary disk contamination by a supernova ejecta is, in the most favorable case, 3 $\times$ 10$^{-3}$