365 research outputs found
Electrochemical Transformation of White Phosphorus as a Way to Compounds With Phosphorus-Hydrogen and Phosphorus-Carbon Bonds
2D Conformal Field Theories and Holography
It is known that the chiral part of any 2d conformal field theory defines a
3d topological quantum field theory: quantum states of this TQFT are the CFT
conformal blocks. The main aim of this paper is to show that a similar CFT/TQFT
relation exists also for the full CFT. The 3d topological theory that arises is
a certain ``square'' of the chiral TQFT. Such topological theories were studied
by Turaev and Viro; they are related to 3d gravity. We establish an
operator/state correspondence in which operators in the chiral TQFT correspond
to states in the Turaev-Viro theory. We use this correspondence to interpret
CFT correlation functions as particular quantum states of the Turaev-Viro
theory. We compute the components of these states in the basis in the
Turaev-Viro Hilbert space given by colored 3-valent graphs. The formula we
obtain is a generalization of the Verlinde formula. The later is obtained from
our expression for a zero colored graph. Our results give an interesting
``holographic'' perspective on conformal field theories in 2 dimensions.Comment: 29+1 pages, many figure
Non-Metric Gravity I: Field Equations
We describe and study a certain class of modified gravity theories. Our
starting point is Plebanski formulation of gravity in terms of a triple B^i of
2-forms, a connection A^i and a ``Lagrange multiplier'' field Psi^ij. The
generalization we consider stems from presence in the action of an extra term
proportional to a scalar function of Psi^ij. As in the usual Plebanski general
relativity (GR) case, a certain metric can be constructed from B^i. However,
unlike in GR, the connection A^i no longer coincides with the self-dual part of
the metric-compatible spin-connection. Field equations of the theory are shown
to be relations between derivatives of the metric and components of field Psi,
as well as its derivatives, the later being in contrast to the GR case. The
equations are of second order in derivatives. An analog of the Bianchi identity
is still present in the theory, as well as its contracted version tantamount to
energy conservation equation.Comment: 21 pages, no figures (v2) energy conservation equation simplified,
note on reality conditions added (v3) minor change
The Fuzzy Sphere Star-Product and Spin Networks
We analyze the expansion of the fuzzy sphere non-commutative product in
powers of the non-commutativity parameter. To analyze this expansion we develop
a graphical technique that uses spin networks. This technique is potentially
interesting in its own right as introducing spin networks of Penrose into
non-commutative geometry. Our analysis leads to a clarification of the link
between the fuzzy sphere non-commutative product and the usual deformation
quantization of the sphere in terms of the star-product.Comment: 21 pages, many figure
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