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

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

Ward Identities for Affine-Virasoro Correlators

Generalizing the Knizhnik-Zamolodchikov equations, we derive a hierarchy of non-linear Ward identities for affine-Virasoro correlators. The hierarchy follows from null states of the Knizhnik-Zamolodchikov type and the assumption of factorization, whose consistency we verify at an abstract level. Solution of the equations requires concrete factorization ans\"atze, which may vary over affine-Virasoro space. As a first example, we solve the non-linear equations for the coset constructions, using a matrix factorization. The resulting coset correlators satisfy first-order linear partial differential equations whose solutions are the coset blocks defined by Douglas.Comment: 53 pages, Latex, LBL-32619, UCB-PTH-92/24, BONN-HE-92/2

Flat Connections and Non-Local Conserved Quantities in Irrational Conformal Field Theory

Irrational conformal field theory (ICFT) includes rational conformal field theory as a small subspace, and the affine-Virasoro Ward identities describe the biconformal correlators of ICFT. We reformulate the Ward identities as an equivalent linear partial differential system with flat connections and new non-local conserved quantities. As examples of the formulation, we solve the system of flat connections for the coset correlators, the correlators of the affine-Sugawara nests and the high-level $n$-point correlators of ICFT.Comment: 40 pages, Latex, UCB-PTH-93/33, LBL-34901, CPTH-A277.129

Solving the Ward Identities of Irrational Conformal Field Theory

The affine-Virasoro Ward identities are a system of non-linear differential equations which describe the correlators of all affine-Virasoro constructions, including rational and irrational conformal field theory. We study the Ward identities in some detail, with several central results. First, we solve for the correlators of the affine-Sugawara nests, which are associated to the nested subgroups $g\supset h_1 \supset \ldots \supset h_n$. We also find an equivalent algebraic formulation which allows us to find global solutions across the set of all affine-Virasoro constructions. A particular global solution is discussed which gives the correct nest correlators, exhibits braiding for all affine-Virasoro correlators, and shows good physical behavior, at least for four-point correlators at high level on simple $g$. In rational and irrational conformal field theory, the high-level fusion rules of the broken affine modules follow the Clebsch-Gordan coefficients of the representations.Comment: 45 pages, Latex, UCB-PTH-93/18, LBL-34111, BONN-HE-93/17. We factorize the biconformal nest correlators of the first version, obtaining the conformal correlators of the affine-Sugawara nests on g/h_1/.../h_

Systematic approach to cyclic orbifolds

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions of conformal field theory and enables us to find the orbifold characters and their modular transformation properties.Comment: 39 pages, LaTeX. v2,3: references added. v4: typos correcte

Semi-Classical Blocks and Correlators in Rational and Irrational Conformal Field Theory

The generalized Knizhnik-Zamolodchikov equations of irrational conformal field theory provide a uniform description of rational and irrational conformal field theory. Starting from the known high-level solution of these equations, we first construct the high-level conformal blocks and correlators of all the affine-Sugawara and coset constructions on simple g. Using intuition gained from these cases, we then identify a simple class of irrational processes whose high-level blocks and correlators we are also able to construct.Comment: 53 pages, Latex. Revised version with extended discussion of phases and secondarie

The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs

We use the Virasoro master equation to study the space of Lie h-invariant conformal field theories, which includes the standard rational conformal field theories as a small subspace. In a detailed example, we apply the general theory to characterize and study the Lie h-invariant graphs, which classify the Lie h-invariant conformal field theories of the diagonal ansatz on SO(n). The Lie characterization of these graphs is another aspect of the recently observed Lie group-theoretic structure of graph theory.Comment: 38p

X-ray Observations and Infrared Identification of the Transient 7.8 s X-ray Binary Pulsar XTE J1829-098

XMM-Newton and Chandra observations of the transient 7.8 s pulsar XTE J1829-098 are used to characterize its pulse shape and spectrum, and to facilitate a search for an optical or infrared counterpart. In outburst, the absorbed, hard X-ray spectrum with Gamma = 0.76+/-0.13 and N_H = (6.0+/-0.6) x 10^{22} cm^{-2} is typical of X-ray binary pulsars. The precise Chandra localization in a faint state leads to the identification of a probable infrared counterpart at R.A. = 18h29m43.98s, decl. = -09o51'23.0" (J2000.0) with magnitudes K=12.7, H=13.9, I>21.9, and R>23.2. If this is a highly reddened O or B star, we estimate a distance of 10 kpc, at which the maximum observed X-ray luminosity is 2x10^{36} ergs s^{-1}, typical of Be X-ray transients or wind-fed systems. The minimum observed luminosity is 3x10^{32}(d/10 kpc)^2 ergs s^{-1}. We cannot rule out the possibility that the companion is a red giant. The two known X-ray outbursts of XTE J1829-098 are separated by ~1.3 yr, which may be the orbital period or a multiple of it, with the neutron star in an eccentric orbit. We also studied a late M-giant long-period variable that we found only 9" from the X-ray position. It has a pulsation period of ~1.5 yr, but is not the companion of the X-ray source.Comment: 6 pages, 7 figures. To appear in The Astrophysical Journa