Vertex Operators in 4D Quantum Gravity Formulated as CFT

We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the ultraviolet limit, which mixes positive-metric and negative-metric modes of the gravitational field and thus these modes cannot be treated separately in physical operators. In this paper, we construct gravitational vertex operators such as the Ricci scalar, defined as space-time volume integrals of them are invariant under conformal transformations. Short distance singularities of these operator products are computed and it is shown that their coefficients have physically correct sign. Furthermore, we show that conformal algebra holds even in the system perturbed by the cosmological constant vertex operator as in the case of the Liouville theory shown by Curtright and Thorn.Comment: 26 pages, rewrote review part concisely, added explanation

Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among well-defined correlators on sphere, but they do not have a beautiful structure that the bosonized theory has and also give an inconsistent result when they include an ill-defined correlator with the divergence. We solve them and compute the several normalization independent ratios of the well-defined correlators, which agree with the matrix model results.Comment: Latex, 22 page

Supersymmetric Wilson Loops in IIB Matrix Model

We show that the supersymmetric Wilson loops in IIB matrix model give a transition operator from reduced supersymmetric Yang-Mills theory to supersymmetric space-time theory. In comparison with Green-Schwarz superstring we identify the supersymmetric Wilson loops with the asymptotic states of IIB superstring. It is pointed out that the supersymmetry transformation law of the Wilson loops is the inverse of that for the vertex operators of massless modes in the U(N) open superstring with Dirichlet boundary condition.Comment: 10 pages, Latex, minor typos correcte

Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. There are no massive ghosts because they are not gauge invariant in this formulation. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.Comment: 51 pages, 12 figure

Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes

On a class of memoryless quantum channels which includes the depolarizing channel, the highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function E(R). The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity.Comment: Ver.4. In vers.1--3, I claimed Theorem 1 for general quantum channels. Now I claim this only for a slight generalization of depolarizing channel in this paper because Lemma 2 in vers.1--3 was wrong; the original general statement is proved in quant-ph/0112103. Ver.5. Text sectionalized. Appeared in PRA. The PRA article is typographically slightly crude: The LaTeX symbol star, used as superscripts, was capriciously replaced by the asterisk in several places after my proof readin

Tema Con Variazioni: Quantum Channel Capacity

Channel capacity describes the size of the nearly ideal channels, which can be obtained from many uses of a given channel, using an optimal error correcting code. In this paper we collect and compare minor and major variations in the mathematically precise statements of this idea which have been put forward in the literature. We show that all the variations considered lead to equivalent capacity definitions. In particular, it makes no difference whether one requires mean or maximal errors to go to zero, and it makes no difference whether errors are required to vanish for any sequence of block sizes compatible with the rate, or only for one infinite sequence.Comment: 32 pages, uses iopart.cl

Evidence of different climatic adaptation strategies in humans and non-human primates

Abstract: To understand human evolution it is critical to clarify which adaptations enabled our colonisation of novel ecological niches. For any species climate is a fundamental source of environmental stress during range expansion. Mammalian climatic adaptations include changes in size and shape reflected in skeletal dimensions and humans fit general primate ecogeographic patterns. It remains unclear however, whether there are also comparable amounts of adaptation in humans, which has implications for understanding the relative importance of biological/behavioural mechanisms in human evolution. We compare cranial variation between prehistoric human populations from throughout Japan and ecologically comparable groups of macaques. We compare amounts of intraspecific variation and covariation between cranial shape and ecological variables. Given equal rates and sufficient time for adaptation for both groups, human conservation of non-human primate adaptation should result in comparable variation and patterns of covariation in both species. In fact, we find similar amounts of intraspecific variation in both species, but no covariation between shape and climate in humans, contrasting with strong covariation in macaques. The lack of covariation in humans may suggest a disconnect in climatic adaptation strategies from other primates. We suggest this is due to the importance of human behavioural adaptations, which act as a buffer from climatic stress and were likely key to our evolutionary success

On Electron Transport in ZrB12, ZrB2 and MgB2

We report on measurements of the temperature dependence of resistivity, $\rho(T)$, for single crystal samples of ZrB$_{12}$, ZrB$_{2}$ and polycrystalline samples of MgB$_{2}$. It is shown that cluster compound ZrB$_{12}$ behaves like a simple metal in the normal state, with a typical Bloch -- Gr\"uneisen $\rho(T)$ dependence. However, the resistive Debye temperature, $T_{R}=300 K$, is three times smaller than $T_{D}$ obtained from specific heat data. We observe the $T^{2}$ term in $\rho(T)$ of these borides, which could be interpreted as an indication of strong electron-electron interaction. Although the $\rho (T)$ dependence of ZrB$_{12}$ reveals a sharp superconductive transition at $T_{c}=6.0 K$, no superconductivity was observed for single crystal samples of ZrB$_{2}$ down to $1.3 K$.Comment: 5 pages, 4 figure

Nontrivial behavior of the Fermi arc in the staggered-flux ordered phase

The doping and temperature dependences of the Fermi arc in the staggered-flux, or the d-density wave, ordered phase of the t-J model are analyzed by the U(1) slave boson theory. Nontrivial behavior is revealed by the self-consistent calculation. At low doped and finite-temperature region, both the length of the Fermi arc and the width of the Fermi pocket are proportional to $\delta$ and the area of the Fermi pocket is proportional to $\delta^2$. This behavior is completely different from that at the zero temperature, where the area of the Fermi pocket becomes $\pi^2 \delta$. This behavior should be observed by detailed experiments of angle-resolved photoemission spectroscopy in the pseudogap phase of high-T_c cuprates if the pseudogap phase is the staggered-flux ordered phase.Comment: 4 pages, 4 figure

Pressure Effects in Manganites with Layered Perovskite Structure

Pressure effects on the charge and spin dynamics in the bilayer manganite compounds $La_{2-2x}Sr_{1+2x}Mn_2O_7$ are studied theoretically by taking into account the orbital degrees of freedom. The orbital degrees are active in the layered crystal structure, and applied hydrostatic pressure stabilizes the $3d_{x^2-y^2}$ orbital in comparison with $3d_{3z^2-r^2}$. The change of the orbital states weakens the interlayer charge and spin couplings, and suppresses the three dimensional ferromagnetic transition. Numerical results, based on an effective Hamiltonian which includes the energy level difference of the orbitals, show that the applied pressure controls the dimensionality of the spin and charge dynamics through changes of the orbital states.Comment: 5 pages, 2 figure