18 research outputs found
Central Charge Reduction and Spacetime Statistics in the Fractional Superstring
Fractional superstrings in the tensor-product formulation experience
``internal projections'' which reduce their effective central charges. Simple
expressions for the characters of the resulting effective worldsheet theory are
found. All states in the effective theory can be consistently assigned definite
spacetime statistics. The projection to the effective theory is shown to be
described by the action of a dimension-three current in the original
tensor-product theory.Comment: 11 pages (LaTeX), CLNS 92/1168, McGill/92-41 (minor typos corrected
New Spin-Two Gauged Sigma Models and General Conformal Field Theory
Recently, we have studied the general Virasoro construction at one loop in
the background of the general non-linear sigma model. Here, we find the action
formulation of these new conformal field theories when the background sigma
model is itself conformal. In this case, the new conformal field theories are
described by a large class of new spin-two gauged sigma models. As examples of
the new actions, we discuss the spin-two gauged WZW actions, which describe the
conformal field theories of the generic affine-Virasoro construction, and the
spin-two gauged g/h coset constructions. We are able to identify the latter as
the actions of the local Lie h-invariant conformal field theories, a large
class of generically irrational conformal field theories with a local gauge
symmetry.Comment: LaTeX, 28 pages, references and clarifying remarks adde
Local Nature of Coset Models
The local algebras of the maximal Coset model C_max associated with a chiral
conformal subtheory A\subset B are shown to coincide with the local relative
commutants of A in B, provided A contains a stress energy tensor.
Making the same assumption, the adjoint action of the unique
inner-implementing representation U^A associated with A\subset B on the local
observables in B is found to define net-endomorphisms of B. This property is
exploited for constructing from B a conformally covariant holographic image in
1+1 dimensions which proves useful as a geometric picture for the joint
inclusion A\vee C_max \subset B.
Immediate applications to the analysis of current subalgebras are given and
the relation to normal canonical tensor product subfactors is clarified. A
natural converse of Borchers' theorem on half-sided translations is made
accessible.Comment: 33 pages, no figures; typos, minor improvement
The Statistical Mechanics of the (2+1)-Dimensional Black Hole
The presence of a horizon breaks the gauge invariance of (2+1)-dimensional
general relativity, leading to the appearance of new physical states at the
horizon. I show that the entropy of the (2+1)-dimensional black hole can be
obtained as the logarithm of the number of these microscopic states.Comment: 12 pages, UCD-94-32 and NI-9401
Maxwell-Chern-Simons Theory With Boundary
The Maxwell-Chern-Simons (MCS) theory with planar boundary is considered. The
boundary is introduced according to Symanzik's basic principles of locality and
separability. A method of investigation is proposed, which, avoiding the
straight computation of correlators, is appealing for situations where the
computation of propagators, modified by the boundary, becomes quite complex.
For MCS theory, the outcome is that a unique solution exists, in the form of
chiral conserved currents, satisfying a Kac-Moody algebra, whose central charge
does not depend on the Maxwell term.Comment: 30 page
Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
We discuss the quantum mechanics and thermodynamics of the (2+1)-dimensional
black hole, using both minisuperspace methods and exact results from
Chern-Simons theory. In particular, we evaluate the first quantum correction to
the black hole entropy. We show that the dynamical variables of the black hole
arise from the possibility of a deficit angle at the (Euclidean) horizon, and
briefly speculate as to how they may provide a basis for a statistical picture
of black hole thermodynamics.Comment: 20 pages and 2 figures, LaTeX, IASSNS-HEP-94/34 and UCD-94-1
Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity
This review contains a summary of work by J.-L. Gervais and the author on the
operator approach to 2d gravity. Special emphasis is placed on the construction
of local observables -the Liouville exponentials and the Liouville field itself
- and the underlying algebra of chiral vertex operators. The double quantum
group structure arising from the presence of two screening charges is discussed
and the generalized algebra and field operators are derived. In the last part,
we show that our construction gives rise to a natural definition of a quantum
tau function, which is a noncommutative version of the classical
group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference
on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199