Gravitational rescue of minimal gauge mediation

Gravity mediation supersymmetry breaking become comparable to gauge mediated supersymmetry breaking contributions when messenger masses are close to the GUT scale. By suitably tuning the gravity contributions one can then modify the soft supersymmetry breaking sector to generate a large stop mixing parameter and a light higgs mass of 125 GeV. In this kind of hybrid models, however the nice features of gauge mediation like flavour conservation etc, are lost. To preserve the nice features, gravitational contributions should become important for lighter messenger masses and should be important only for certain fields. This is possible when the hidden sector contains multiple (at least two) spurions with hierarchical vaccum expectation values. In this case, the gravitational contribtutions can be organised to be `just right'. We present a complete model with two spurion hidden sector where the gravitational contribution is from a warped flavour model in a Randall-Sundrum setting. Along the way, we present simple expressions to handle renormalisation group equations when supersymmetry is broken by two different sectors at two different scales.Comment: 24 Pages, 3 figures, Detailed discussions on flavour violation included, added figure and references, Matches published versio

First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories

The first law of black hole mechanics is derived from the Einstein-Maxwell (EM) Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills (EYM) theory is also derived.Comment: Modified version, major changes made in the introduction. 14 pages, no figur

On the Noether charge form of the first law of black hole mechanics

The first law of black hole mechanics was derived by Wald in a general covariant theory of gravity for stationary variations around a stationary black hole. It is formulated in terms of Noether charges, and has many advantages. In this paper several issues are discussed to strengthen the validity of the Noether charge form of the first law. In particular, a gauge condition used in the derivation is justified. After that, we justify the generalization to non-stationary variations done by Iyer-Wald.Comment: Latex, 16 pages, arguments on gauge conditions and near-stationary entropy are added, accepted for publication in Physical Review

Lagrangian perfect fluids and black hole mechanics

The first law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial infinity, of a stationary, axisymmetric black hole, in a diffeomorphism invariant Lagrangian theory of gravity. The original statement of the first law given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system contained, in addition, volume integrals of the fluid fields, over a spacelike slice stretching between these two surfaces. When applied to the Einstein-perfect fluid system, however, Wald's methods yield restricted results. The reason is that the fluid fields in the Lagrangian of a gravitating perfect fluid are typically nonstationary. We therefore first derive a first law-like relation for an arbitrary Lagrangian metric theory of gravity coupled to arbitrary Lagrangian matter fields, requiring only that the metric field be stationary. This relation includes a volume integral of matter fields over a spacelike slice between the black hole horizon and spatial infinity, and reduces to the first law originally derived by Bardeen, Carter and Hawking when the theory is general relativity coupled to a perfect fluid. We also consider a specific Lagrangian formulation for an isentropic perfect fluid given by Carter, and directly apply Wald's analysis. The resulting first law contains only surface integrals at the black hole horizon and spatial infinity, but this relation is much more restrictive in its allowed fluid configurations and perturbations than that given by Bardeen, Carter and Hawking. In the Appendix, we use the symplectic structure of the Einstein-perfect fluid system to derive a conserved current for perturbations of this system: this current reduces to one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2

Efficient simulations with electronic open boundaries

We present a reformulation of the Hairy Probe method for introducing electronic open boundaries that is appropriate for steady state calculations involving non-orthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms, and a perfect non-orthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit, and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean inter-level spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene, and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the π-conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current

Stability of geometrically frustrated magnetic state of Ca3CoRhO6 to applications of positive and negative pressure

The influence of negative chemical pressure induced by gradual replacement of Ca by Sr as well as of external pressure (up to 10 kbar) on the magnetism of Ca3CoRhO6 has been investigated by magnetization studies. It is found that the solid solution, Ca(3-x)Sr(x)CoRhO6, exists at least till about x= 1.0 without any change in the crystal structure. Apart from insensitivity of the spin-chain feature to volume expansion, the characteristic features of geometrical frustration interestingly appear at the same temperatures for all compositions, in sharp contrast to the response to Y substitution for Ca (reported previously). Interestingly, huge frequency dependence of ac susceptibility known for the parent compound persists for all compositions. We do not find a change in the properties under external pressure. The stability of the magnetic anomalies of this compound to the volume change (about 4%) is puzzling

Entropy of Constant Curvature Black Holes in General Relativity

We consider the thermodynamic properties of the constant curvature black hole solution recently found by Banados. We show that it is possible to compute the entropy and the quasilocal thermodynamics of the spacetime using the Einstein-Hilbert action of General Relativity. The constant curvature black hole has some unusual properties which have not been seen in other black hole spacetimes. The entropy of the black hole is not associated with the event horizon; rather it is associated with the region between the event horizon and the observer. Further, surfaces of constant internal energy are not isotherms so the first law of thermodynamics exists only in an integral form. These properties arise from the unusual topology of the Euclidean black hole instanton.Comment: 4 pages LaTeX2e (RevTeX), 2 PostScript figures. Small corrections in the text and the reference

Evolutionary connection between the catalytic subunits of DNA-dependent RNA polymerases and eukaryotic RNA-dependent RNA polymerases and the origin of RNA polymerases

BACKGROUND: The eukaryotic RNA-dependent RNA polymerase (RDRP) is involved in the amplification of regulatory microRNAs during post-transcriptional gene silencing. This enzyme is highly conserved in most eukaryotes but is missing in archaea and bacteria. No evolutionary relationship between RDRP and other polymerases has been reported so far, hence the origin of this eukaryote-specific polymerase remains a mystery. RESULTS: Using extensive sequence profile searches, we identified bacteriophage homologs of the eukaryotic RDRP. The comparison of the eukaryotic RDRP and their homologs from bacteriophages led to the delineation of the conserved portion of these enzymes, which is predicted to harbor the catalytic site. Further, detailed sequence comparison, aided by examination of the crystal structure of the DNA-dependent RNA polymerase (DDRP), showed that the RDRP and the β' subunit of DDRP (and its orthologs in archaea and eukaryotes) contain a conserved double-psi β-barrel (DPBB) domain. This DPBB domain contains the signature motif DbDGD (b is a bulky residue), which is conserved in all RDRPs and DDRPs and contributes to catalysis via a coordinated divalent cation. Apart from the DPBB domain, no similarity was detected between RDRP and DDRP, which leaves open two scenarios for the origin of RDRP: i) RDRP evolved at the onset of the evolution of eukaryotes via a duplication of the DDRP β' subunit followed by dramatic divergence that obliterated the sequence similarity outside the core catalytic domain and ii) the primordial RDRP, which consisted primarily of the DPBB domain, evolved from a common ancestor with the DDRP at a very early stage of evolution, during the RNA world era. The latter hypothesis implies that RDRP had been subsequently eliminated from cellular life forms and might have been reintroduced into the eukaryotic genomes through a bacteriophage. Sequence and structure analysis of the DDRP led to further insights into the evolution of RNA polymerases. In addition to the β' subunit, β subunit of DDRP also contains a DPBB domain, which is, however, distorted by large inserts and does not harbor a counterpart of the DbDGD motif. The DPBB domains of the two DDRP subunits together form the catalytic cleft, with the domain from the β' subunit supplying the metal-coordinating DbDGD motif and the one from the β subunit providing two lysine residues involved in catalysis. Given that the two DPBB domains of DDRP contribute completely different sets of active residues to the catalytic center, it is hypothesized that the ultimate ancestor of RNA polymerases functioned as a homodimer of a generic, RNA-binding DPBB domain. This ancestral protein probably did not have catalytic activity and served as a cofactor for a ribozyme RNA polymerase. Subsequent evolution of DDRP and RDRP involved accretion of distinct sets of additional domains. In the DDRPs, these included a RNA-binding Zn-ribbon, an AT-hook-like module and a sandwich-barrel hybrid motif (SBHM) domain. Further, lineage-specific accretion of SBHM domains and other, DDRP-specific domains is observed in bacterial DDRPs. In contrast, the orthologs of the β' subunit in archaea and eukaryotes contains a four-stranded α + β domain that is shared with the α-subunit of bacterial DDRP, eukaryotic DDRP subunit RBP11, translation factor eIF1 and type II topoisomerases. The additional domains of the RDRPs remain to be characterized. CONCLUSIONS: Eukaryotic RNA-dependent RNA polymerases share the catalytic double-psi β-barrel domain, containing a signature metal-coordinating motif, with the universally conserved β' subunit of DNA-dependent RNA polymerases. Beyond this core catalytic domain, the two classes of RNA polymerases do not have common domains, suggesting early divergence from a common ancestor, with subsequent independent domain accretion. The β-subunit of DDRP contains another, highly diverged DPBB domain. The presence of two distinct DPBB domains in two subunits of DDRP is compatible with the hypothesis that the ultimate ancestor of RNA polymerases was a RNA-binding DPBB domain that had no catalytic activity but rather functioned as a homodimeric cofactor for a ribozyme polymerase

A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes

The entropy of stationary black holes has recently been calculated by a number of different approaches. Here we compare the Noether charge approach (defined for any diffeomorphism invariant Lagrangian theory) with various Euclidean methods, specifically, (i) the microcanonical ensemble approach of Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and Zanelli which ultimately expresses black hole entropy in terms of the Hilbert action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli (also used by Susskind and Uglum) which views black hole entropy as conjugate to a conical deficit angle, and (iv) the pair creation approach of Garfinkle, Giddings, and Strominger. All of these approaches have a more restrictive domain of applicability than the Noether charge approach. Specifically, approaches (i) and (ii) appear to be restricted to a class of theories satisfying certain properties listed in section 2; approach (iii) appears to require the Lagrangian density to be linear in the curvature; and approach (iv) requires the existence of suitable instanton solutions. However, we show that within their domains of applicability, all of these approaches yield results in agreement with the Noether charge approach. In the course of our analysis, we generalize the definition of Brown and York's quasilocal energy to a much more general class of diffeomorphism invariant, Lagrangian theories of gravity. In an appendix, we show that in an arbitrary diffeomorphism invariant theory of gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a time evolution vector field $t^a$ always can be expressed as the spatial integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late