The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26c=26 III. The Spectra of c^=52\hat{c}=52 Strings

In the second paper of this series, I obtained the twisted BRST systems and extended physical-state conditions of all twisted open and closed $\hat{c} = 52$ strings. In this paper, I supplement the extended physical-state conditions with the explicit form of the extended (twisted) Virasoro generators of all $\hat{c} = 52$ strings, which allows us to discuss the physical spectra of these systems. Surprisingly, all the $\hat{c}=52$ spectra admit an equivalent description in terms of generically-unconventional Virasoro generators at $c=26$. This description strongly supports our prior conjecture that the $\hat{c}=52$ strings are free of negative-norm states, and moreover shows that the spectra of some of the simpler cases are equivalent to those of ordinary untwisted open and closed $c=26$ strings.Comment: 23 page

The Orbifold-String Theories of Permutation-Type: I. One Twisted BRST per Cycle per Sector

We resume our discussion of the new orbifold-string theories of permutation-type, focusing in the present series on the algebraic formulation of the general bosonic prototype and especially the target space-times of the theories. In this first paper of the series, we construct one twisted BRST system for each cycle $j$ in each twisted sector $\sigma$ of the general case, verifying in particular the previously-conjectured algebra $[Q_{i}(\sigma),Q_{j}(\sigma)]_{+} =0$ of the BRST charges. The BRST systems then imply a set of extended physical-state conditions for the matter of each cycle at cycle central charge $\hat{c}_{j}(\sigma)=26f_{j}(\sigma)$ where $f_{j}(\sigma)$ is the length of cycle $j$.Comment: 31 page

W3 Constructions on Affine Lie Algebras

We use an argument of Romans showing that every Virasoro construction leads to realizations of $W_3$, to construct $W_3$ realizations on arbitrary affine Lie algebras. Solutions are presented for generic values of the level as well as for specific values of the level but with arbitrary parameters. We give a detailed discussion of the \aff{su}(2)_\ell-case. Finally, we discuss possible applications of these realizations to the construction of $W$-strings.Comment: 9 page

On the Target-Space Geometry of Open-String Orientation-Orbifold Sectors

Including world-sheet orientation-reversing automorphisms in the orbifold program, we recently reported the twisted operator algebra and twisted KZ equations in each open-string sector of the general WZW orientation orbifold. In this paper we work out the corresponding classical description of these sectors, including the {\it WZW orientation-orbifold action} -- which is naturally defined on the solid half cylinder -- and its associated WZW orientation-orbifold branes. As a generalization, we also obtain the {\it sigma-model orientation-orbifold action}, which describes a much larger class of open-string orientation-orbifold sectors. As special cases, this class includes twisted open-string {\it free boson} examples, the open-string WZW sectors above and the open-string sectors of the {\it general coset orientation orbifold}. Finally, we derive the {\it orientation- orbifold Einstein equations}, in terms of twisted Einstein tensors -- which hold when the twisted open-string sigma-model sectors are 1-loop conformal.Comment: 77 pages, typos correcte

Conformal Models of Thirring Type and the Affine Virasoro Construction

We investigate a class of models in 1+1 dimensions with four fermion interaction term. At each order of the perturbation expansion, the models are ultraviolet finite and Lorentz non-invariant. We show that for certain privileged values of the coupling constants, Lorentz symmetry is restored, and indeed the model turns out to be conformally invariant. This phenomenon is both quantum mechanical and non-perturbative.Comment: 14 pages, Latex. Some numerical errors have been correcte

The Orbifold-String Theories of Permutation-Type: III. Lorentzian and Euclidean Space-Times in a Large Example

To illustrate the general results of the previous paper, we discuss here a large concrete example of the orbifold-string theories of permutation-type. For each of the many subexamples, we focus on evaluation of the \emph{target space-time dimension} $\hat{D}_j(\sigma)$, the \emph{target space-time signature} and the \emph{target space-time symmetry} of each cycle $j$ in each twisted sector $\sigma$. We find in particular a gratifying \emph{space-time symmetry enhancement} which naturally matches the space-time symmetry of each cycle to its space-time dimension. Although the orbifolds of $\Z_{2}$-permutation-type are naturally Lorentzian, we find that the target space-times associated to larger permutation groups can be Lorentzian, Euclidean and even null (\hat{D}_{j}(\sigma)=0), with varying space-time dimensions, signature and symmetry in a single orbifold.Comment: 36 page

Detection of an X-ray Pulsation for the Gamma-ray Pulsar Centered in CTA 1

We report the detection of X-ray pulsations with a period of ~315.87 ms from the 2009 XMM-Newton observation for the radio-quiet gamma-ray pulsar, LAT PSR J0007+7303, centered in the supernova remnant CTA 1. The detected pulsed period is consistent with the gamma-ray periodicity at the same epoch found with the Fermi Gamma-ray Space Telescope. The broader sinusoidal structure in the folded light curve of the X-ray emission is dissimilar to that of the gamma-ray emission, and the phase of the peak is about 0.5 shifting from the peak in the gamma-ray bands, indicating that the main component of the X-rays originates from different sites of the pulsar. We conclude that the main component of the X-ray pulsation is contributed by the thermal emission from the neutron star. Although with a significantly different characteristic age, PSR~J0007+7303 is similar to Geminga in emission properties of X-rays and gamma-rays; this makes PSR J0007+7303 the second radio-quiet gamma-ray pulsar with detected X-ray pulsations after Geminga.Comment: 7 pages, 4 figures and 1 table; accepted by ApJ

Nonsemisimple Sugawara Constructions

By a Sugawara construction we mean a generalized Virasoro construction in which the currents are primary fields of conformal weight one. For simple Lie algebras, this singles out the standard Sugawara construction out of all the solutions to the Virasoro master equation. Examples of nonsemisimple Sugawara constructions have appeared recently. They share the properties that the Virasoro central charge is an integer equal to the dimension of the Lie algebra and that they can be obtained by high-level contraction of reductive Sugawara constructions: they thus correspond to free bosons. Exploiting a recent structure theorem for Lie algebras with an invariant metric, we are able to unify all the known constructions under the same formalism and, at the same time, to prove several results about the Sugawara constructions. In particular, we prove that all such constructions factorize into a standard (semisimple) Sugawara construction and a nonsemisimple one (with integral central charge) of a form which generalizes the nonsemisimple examples known so far.Comment: uuencoded compressed .dvi file (needs AMSFonts 2.1+), 13 document pages but 7 physical page

Energy Distribution of a Charged Black Hole with a Minimally Coupled Scalar Field

Using three different energy-momentum complexes, the Einstein, Landau-Lifshitz, and Papapetrou prescriptions, we calculate the energy of an electrically charged black hole exact solution with a self-interacting, minimally-coupled scalar field and the asymptotic region locally an Anti-deSitter spacetime. Writing the metric in Kerr-Schild Cartesian coordinates, we demonstrate that this metric belongs to the Kerr-Schild class of solutions. Applying each of the three energy-momentum prescriptions and comparing the results, we find consistency among these complexes, suggesting their utility as localized measures of energy.Comment: 11 pages; To appear in Astrophysics and Space Scienc