5,690 research outputs found
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} , the \emph{target space-time
signature} and the \emph{target space-time symmetry} of each cycle in each
twisted sector . 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
-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
The orbifold-string theories of permutation-type: II. Cycle dynamics and target space-time dimensions
We continue our discussion of the general bosonic prototype of the new
orbifold-string theories of permutation type. Supplementing the extended
physical-state conditions of the previous paper, we construct here the extended
Virasoro generators with cycle central charge
, where is the length of cycle
in twisted sector . We also find an equivalent, reduced formulation
of each physical-state problem at reduced cycle central charge
. These tools are used to begin the study of the target
space-time dimension of cycle in sector , which
is naturally defined as the number of zero modes (momenta) of each cycle. The
general model-dependent formulae derived here will be used extensively in
succeeding papers, but are evaluated in this paper only for the simplest case
of the "pure" permutation orbifolds.Comment: 32 page
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
Two photon excitation as a tool for atmospheric and kinetic research
Progress was made in the following areas: two photon excitation cross section of hydroxyl, marker fringe generation of deep UV and VUV radiation, and CN radiative lifetimes
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 in each twisted sector of the general case,
verifying in particular the previously-conjectured algebra
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 where
is the length of cycle .Comment: 31 page
Unified Einstein-Virasoro Master Equation in the General Non-Linear Sigma Model
The Virasoro master equation (VME) describes the general affine-Virasoro
construction T=L^{ab}J_aJ_b+iD^a \dif J_a in the operator algebra of the WZW
model, where is the inverse inertia tensor and is the
improvement vector. In this paper, we generalize this construction to find the
general (one-loop) Virasoro construction in the operator algebra of the general
non-linear sigma model. The result is a unified Einstein-Virasoro master
equation which couples the spacetime spin-two field to the background
fields of the sigma model. For a particular solution , the unified
system reduces to the canonical stress tensors and conventional Einstein
equations of the sigma model, and the system reduces to the general
affine-Virasoro construction and the VME when the sigma model is taken to be
the WZW action. More generally, the unified system describes a space of
conformal field theories which is presumably much larger than the sum of the
general affine-Virasoro construction and the sigma model with its canonical
stress tensors. We also discuss a number of algebraic and geometrical
properties of the system, including its relation to an unsolved problem in the
theory of -structures on manifolds with torsion.Comment: LaTeX, 55 pages, one postscript figure, uses epsfig.sty. contains a
few minor corrections; version to be published in Int. J. Mod. Phys.
Unification of the General Non-Linear Sigma Model and the Virasoro Master Equation
The Virasoro master equation describes a large set of conformal field
theories known as the affine-Virasoro constructions, in the operator algebra
(affine Lie algebra) of the WZW model, while the Einstein equations of the
general non-linear sigma model describe another large set of conformal field
theories. This talk summarizes recent work which unifies these two sets of
conformal field theories, together with a presumable large class of new
conformal field theories. The basic idea is to consider spin-two operators of
the form in the background of a general
sigma model. The requirement that these operators satisfy the Virasoro algebra
leads to a set of equations called the unified Einstein-Virasoro master
equation, in which the spin-two spacetime field couples to the usual
spacetime fields of the sigma model. The one-loop form of this unified system
is presented, and some of its algebraic and geometric properties are discussed.Comment: 18 pages, Latex. Talk presented by MBH at the NATO Workshop `New
Developments in Quantum Field Theory', June 14-20, 1997, Zakopane, Polan
The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 IV. Orientation Orbifolds Include Orientifolds
In this fourth paper of the series, I clarify the somewhat mysterious
relation between the large class of {\it orientation orbifolds} (with twisted
open-string CFT's at ) and {\it orientifolds} (with untwisted open
strings at ), both of which have been associated to division by
world-sheet orientation-reversing automorphisms. In particular -- following a
spectral clue in the previous paper -- I show that, even as an {\it interacting
string system}, a certain half-integer-moded orientation orbifold-string system
is in fact equivalent to the archetypal orientifold. The subtitle of this
paper, that orientation orbifolds include and generalize standard orientifolds,
then follows because there are many other orientation orbifold-string systems
-- with higher fractional modeing -- which are not equivalent to untwisted
string systems.Comment: 22 pages, typos correcte
The Algebras of Large N Matrix Mechanics
Extending early work, we formulate the large N matrix mechanics of general
bosonic, fermionic and supersymmetric matrix models, including Matrix theory:
The Hamiltonian framework of large N matrix mechanics provides a natural
setting in which to study the algebras of the large N limit, including
(reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We
find in particular a broad array of new free algebras which we call symmetric
Cuntz algebras, interacting symmetric Cuntz algebras, symmetric
Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the
role of these algebras in solving the large N theory. Most important, the
interacting Cuntz algebras are associated to a set of new (hidden) local
quantities which are generically conserved only at large N. A number of other
new large N phenomena are also observed, including the intrinsic nonlocality of
the (reduced) trace class operators of the theory and a closely related large N
field identification phenomenon which is associated to another set (this time
nonlocal) of new conserved quantities at large N.Comment: 70 pages, expanded historical remark
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