SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity

We consider a space-time with spatial sections isomorphic to the group manifold of SU(2). Triad and connection fluctuations are assumed to be SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform non-perturbative path integral quantization of the model. Contarary to previous claims the path integral measure appeared to be non-singular near configurations admitting additional Killing vectors. In this model we are able to calculate the generating functional of Green functions of the reduced phase space variables exactly.Comment: 12 page

Constants of motion for vacuum general relativity

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the $SL(2,R)$ principal chiral model with certain `source' terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as explicit functionals on the phase space of Einstein gravity, and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices

A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centraliser of this action a quantum algebra (a quasi-triangular Hopf algebra) U_q with a representation ring equivalent to the representation ring of the sl_2 Lie algebra. This algebra U_q is the symmetry algebra of the corresponding open spin chain.Comment: 14 pages LaTex; typos corrected and two references adde

Singularities of nn-fold integrals of the Ising class and the theory of elliptic curves

We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for $n=1, 2, 3, 4$ and only modulo some primes for $n=5$ and $6$, thus providing a large set of (possible) new singularities of the $\chi^{(n)}$. We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to $n= 6$) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a {\em finite number of one dimensional integrals}. Among the singularities found, we underline the fact that the quadratic polynomial condition $1+3 w +4 w^2 = 0$, that occurs in the linear differential equation of $\chi^{(3)}$, actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure

Direct evidence for shock-powered optical emission in a nova

Classical novae are thermonuclear explosions that occur on the surfaces of white dwarf stars in interacting binary systems1. It has long been thought that the luminosity of classical novae is powered by continued nuclear burning on the surface of the white dwarf after the initial runaway2. However, recent observations of gigaelectronvolt γ-rays from classical novae have hinted that shocks internal to the nova ejecta may dominate the nova emission. Shocks have also been suggested to power the luminosity of events as diverse as stellar mergers3, supernovae4 and tidal disruption events5, but observational confirmation has been lacking. Here we report simultaneous space-based optical and γ-ray observations of the 2018 nova V906 Carinae (ASASSN-18fv), revealing a remarkable series of distinct correlated flares in both bands. The optical and γ-ray flares occur simultaneously, implying a common origin in shocks. During the flares, the nova luminosity doubles, implying that the bulk of the luminosity is shock powered. Furthermore, we detect concurrent but weak X-ray emission from deeply embedded shocks, confirming that the shock power does not appear in the X-ray band and supporting its emergence at longer wavelengths. Our data, spanning the spectrum from radio to γ-ray, provide direct evidence that shocks can power substantial luminosity in classical novae and other optical transients

Whole-genome sequencing of multiple myeloma reveals oncogenic pathways are targeted somatically through multiple mechanisms.

Multiple myeloma (MM) is a biologically heterogeneous malignancy, however, the mechanisms underlying this complexity are incompletely understood. We report an analysis of the whole-genome sequencing of 765 MM patients from CoMMpass. By employing promoter capture Hi-C in naïve B-cells, we identify cis-regulatory elements (CREs) that represent a highly enriched subset of the non-coding genome in which to search for driver mutations. We identify regulatory regions whose mutation significantly alters the expression of genes as candidate non-coding drivers, including copy number variation (CNV) at CREs of MYC and single-nucleotide variants (SNVs) in a PAX5 enhancer. To better inform the interplay between non-coding driver mutations with other driver mechanisms, and their respective roles in oncogenic pathways, we extended our analysis identifying coding drivers in 40 genes, including 11 novel candidates. We demonstrate the same pathways can be targeted by coding and non-coding mutations; exemplified by IRF4 and PRDM1, along with BCL6 and PAX5, genes that are central to plasma cell differentiation. This study reveals new insights into the complex genetic alterations driving MM development and an enhanced understanding of oncogenic pathways