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

The WZW Model as a Dynamical System on Affine Lie Groups

Working directly on affine Lie groups, we construct several new formulations of the WZW model. In one formulation WZW is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation WZW is written as a two-dimensional field theory, with a three-dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional WZW formulation on the Lie group. Using this dictionary, we also express WZW as a three-dimensional field theory on the Lie group with a four-dimensional WZW term.Comment: 46 pages, Late

The connection between non-exponential relaxation and fragility in supercooled liquids

Among the outstanding problems in the theory of supercooled liquids are the reasons for the rapid increase in their viscosity and relaxation times as the temperature is lowered towards the glass transition temperature, the non-exponential time dependence of the relaxation, and the possible connection between these two properties. The ferromagnetic Potts model on a square latice is a simple system that is found to exhibit these properties. Our calculations show that in this system the connection between them is associated with the dependence on temperature and time of the average environment of the sites. Some of the consequences of this for understanding the behavior of supercooled liquids are discussed.Comment: 12 pages, 8 figure

Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)

Recently the operator algebra and twisted vertex operator equations were given for each sector of all WZW orbifolds, and a set of twisted KZ equations for the WZW permutation orbifolds were worked out as a large example. In this companion paper we report two further large examples of this development. In the first example we solve the twisted vertex operator equations in an abelian limit to obtain the twisted vertex operators and correlators of a large class of abelian orbifolds. In the second example, the twisted vertex operator equations are applied to obtain a set of twisted KZ equations for the (outer-automorphic) charge conjugation orbifold on su(n \geq 3).Comment: 58 pages, v2: three minor typo

Flow equation for Halpern-Huang directions of scalar O(N) models

A class of asymptotically free scalar theories with O(N) symmetry, defined via the eigenpotentials of the Gaussian fixed point (Halpern-Huang directions), are investigated using renormalization group flow equations. Explicit solutions for the form of the potential in the nonperturbative infrared domain are found in the large-N limit. In this limit, potentials without symmetry breaking essentially preserve their shape and undergo a mass renormalization which is governed only by the renormalization group distance parameter; as a consequence, these scalar theories do not have a problem of naturalness. Symmetry-breaking potentials are found to be ``fine-tuned'' in the large-N limit in the sense that the nontrivial minimum vanishes exactly in the limit of vanishing infrared cutoff: therefore, the O(N) symmetry is restored in the quantum theory and the potential becomes flat near the origin.Comment: 18 pages, 4 figures, LaTeX, references added, presentation improved, final version to appear in Phys. Rev.

E 0336-248 : A New BL Lac Object Found by an Old Einstein

We obtained new ROSAT HRI and optical observations in the field of the Einstein X-ray source E 0336-248, which we use to identify it as a 19th magnitude BL Lacertae object at z=0.251 with an X-ray luminosity of 10^45 erg/s. It is also a 14 mJy radio source at 20 cm. An emission-line galaxy at z=0.043 that was previously considered a Seyfert identification for E 0336-248 is shown instead to be an unrelated, non-active H II region galaxy that lies 78 arcseconds from the X-ray source. The resolution of this historical case of mistaken identity illustrates that discoveries of non-AGN emission-line galaxies with high X-ray luminosity should be tested carefully. The properties of E 0336-248 are similar to those of other X-ray selected BL Lacs, including its location in an apparent group or cluster of galaxies. Somewhat unusual is the weak contribution of nonstellar optical light relative to the starlight in the spectrum of its host galaxy, which raises once again the possibility that even high-luminosity BL Lac objects may be difficult to identify in X-ray selected samples. We discuss a possible manifestation of this problem that appeared in the recent literature.Comment: To appear in the Astronomical Journal. 8 pages including figures (uses psfig.tex, also included

On the Fixed-Point Structure of Scalar Fields

In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526), certain properties of the Local Potential Approximation (LPA) to the Wilson renormalization group were uncovered, which led the authors to conclude that $D>2$ dimensional scalar field theories endowed with {\sl non-polynomial} interactions allow for a continuum of renormalization group fixed points, and that around the Gaussian fixed point, asymptotically free interactions exist. If true, this could herald very important new physics, particularly for the Higgs sector of the Standard Model. Continuing work in support of these ideas, has motivated us to point out that we previously studied the same properties and showed that they lead to very different conclusions. Indeed, in as much as the statements in hep-th/9406199 are correct, they point to some deep and beautiful facts about the LPA and its generalisations, but however no new physics.Comment: Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1 page, 1 eps figure, uses LaTeX, RevTex and eps

Computations in Large N Matrix Mechanics

The algebraic formulation of Large N matrix mechanics recently developed by Halpern and Schwartz leads to a practical method of numerical computation for both action and Hamiltonian problems. The new technique posits a boundary condition on the planar connected parts X_w, namely that they should decrease rapidly with increasing order. This leads to algebraic/variational schemes of computation which show remarkably rapid convergence in numerical tests on some many- matrix models. The method allows the calculation of all moments of the ground state, in a sequence of approximations, and excited states can be determined as well. There are two unexpected findings: a large d expansion and a new selection rule for certain types of interaction.Comment: 27 page

ROSAT PSPC and Hri Observations of the Composite Starburst/Seyfert 2 Galaxy NGC 1672

The nearby barred spiral galaxy NGC 1672 is thought to have a weak Seyfert nucleus in addition to its strong starburst activity. Observations with the PSPC and HRI instruments on board the ROSAT X-ray satellite show that three X-ray sources with luminosities (1--2)\times 10^{40} erg/s are clearly identified with NGC 1672. The strongest X-ray source lies at the nucleus, and the other two lie near the ends of the prominent bar, locations that are also bright in H-alpha and near-infrared images. The nuclear source is resolved by the HRI on about the scale of the recently identified nuclear ring, and one of the sources at the ends of the bar is also probably resolved. The X-ray spectrum of the nuclear source is quite soft, having a Raymond--Smith plasma temperature of about 0.7 keV and little evidence for intrinsic absorption. The ROSAT band X-ray flux of the nuclear source appears to be dominated not by X-ray binary emission but rather by diffuse gas emission. While the properties of the nuclear source are generally supportive of a superbubble interpretation, its large density and emission measure stretch the limits that can be comfortably accommodated by such models. We do not detect direct emission from the putative Seyfert nucleus, although an alternative model for the nuclear source is thermal emission from gas that is photoionized by a hidden Seyfert nucleus. The spectra of the other two X-ray sources are harder than that of the nuclear source, and superbubble models for them have the same strengths and weaknesses.Comment: 11 pages, uuencoded compressed postscript, MNRAS in pres