Heterotic supergravity with internal almostKähler spaces; instantons for SO(32) AbstractThe goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/ (super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such Made open access 13 September 2017Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P SL(2, Z) correspond to d-fold M 3 -coverings over the trefoil knot. In this paper, one also investigates quantum information on a few 'universal' knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M 3 's obtained from Dehn fillings are explored.

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G=Z5⋊H where H=Z2.S4≅2O is isomorphic to the binary octahedral group 2O and S4 is the symmetric group on four letters/bases. The second group has signature G=Z5⋊GL(2,3) and points out a threefold symmetry of base pairings. For those groups, the representations for the 22 conjugacy classes of G are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the 22 characters of G attached to those representations are informationally complete. The biological meaning of these coincidences is discussed.

We propose a mechanism displaying confinement, as defined by the behavior of the propagators, for 4 dimensional, N = 1 supersymmetric Yang-Mills theory in superfield formalism. In this work we intend to verify the possibility of extending the known Gribov problem of quantization of Yang-Mills theories and the implementation of a local action with auxiliary superfields like Gribov-Zwanziger approach to this problem. * macielamaral@uerj.br †

It is shown that the representation theory of some finitely presented groups thanks to their SL2(C) character variety is related to algebraic surfaces. We make use of the Enriques–Kodaira classification of algebraic surfaces and related topological tools to make such surfaces explicit. We study the connection of SL2(C) character varieties to topological quantum computing (TQC) as an alternative to the concept of anyons. The Hopf link H, whose character variety is a Del Pezzo surface fH (the trace of the commutator), is the kernel of our view of TQC. Qutrit and two-qubit magic state computing, derived from the trefoil knot in our previous work, may be seen as TQC from the Hopf link. The character variety of some two-generator Bianchi groups, as well as that of the fundamental group for the singular fibers E˜6 and D˜4 contain fH. A surface birationally equivalent to a K3 surface is another compound of their character varieties.