10,530 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
Infinite Dimensional Free Algebra and the Forms of the Master Field
We find an infinite dimensional free algebra which lives at large N in any
SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural
basis of this algebra is a free-algebraic generalization of Chebyshev
polynomials and the dual basis is closely related to the planar connected
parts. This leads to a number of free-algebraic forms of the master field
including an algebraic derivation of the Gopakumar-Gross form. For action
theories, these forms of the master field immediately give a number of new
free-algebraic packagings of the planar Schwinger-Dyson equations.Comment: 39 pages. Expanded historical remark
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
Recent Progress in Irrational Conformal Field Theory
In this talk, I will review the foundations of irrational conformal field
theory (ICFT), which includes rational conformal field theory as a small
subspace. Highlights of the review include the Virasoro master equation, the
Ward identities for the correlators of ICFT and solutions of the Ward
identities. In particular, I will discuss the solutions for the correlators of
the coset constructions and the correlators of the affine-Sugawara nests
on . Finally, I will discuss the
recent global solution for the correlators of all the ICFT's in the master
equation.Comment: 16 pages, Latex, UCB-PTH-93/25, LBL-34610, talk presented at the
conference "Strings 1993", Berkeley, May 23-2
The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 II. The Twisted BRST Systems of \hatc=52 Matter
This is the second in a series of papers which consider the orbifolds of
permutation-type as candidates for new physical string systems at higher
central charge. In the first paper, I worked out the extended actions of the
twisted sectors of these orbifolds -- which exhibit new permutation-twisted
world-sheet gravities and correspondingly extended diffeomorphism groups. In
this paper I begin the study of these systems as operator string theories,
limiting the discussion for simplicity to the strings with
matter (which are those governed by -twisted permutation
gravity). In particular, I present here a construction of the twisted
reparametrization ghosts and {\em new twisted BRST systems} of all strings. The twisted BRST systems also imply new {\em extended physical
state conditions}, whose analysis for individual strings is
deferred to the next paper of the series.Comment: 21 pages, reference added and typos correcte
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
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