243 research outputs found
Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))
The decomposition of tensor products of representations into irreducibles is
studied for a continuous family of integrable operator representations of
. It is described by an explicit integral transformation involving
a distributional kernel that can be seen as an analogue of the Clebsch-Gordan
coefficients. Moreover, we also study the relation between two canonical
decompositions of triple tensor products into irreducibles. It can be
represented by an integral transformation with a kernel that generalizes the
Racah-Wigner coefficients. This kernel is explicitly calculated.Comment: 39 pages, AMS-Latex; V2: Added comments and references concerning
relation to Faddeev's modular double, minor corrections, version to be
published in CM
Liouville bootstrap via harmonic analysis on a noncompact quantum group
The purpose of this short note is to announce results that amount to a
verification of the bootstrap for Liouville theory in the generic case under
certain assumptions concerning existence and properties of fusion
transformations. Under these assumptions one may characterize the fusion and
braiding coefficients as solutions of a system of functional equations that
follows from the combination of consistency requirements and known results.
This system of equations has a unique solution for irrational central charge
c>25. The solution is constructed by solving the Clebsch-Gordan problem for a
certain continuous series of quantum group representations and constructing the
associated Racah-coefficients. This gives an explicit expression for the fusion
coefficients. Moreover, the expressions can be continued into the strong
coupling region 1<c<25, providing a solution of the bootstrap also for this
region.Comment: 16 pages, typos removed incl. important one in (48
Boundary Liouville Field Theory: Boundary Three Point Function
Liouville field theory is considered on domains with conformally invariant
boundary conditions. We present an explicit expression for the three point
function of boundary fields in terms of the fusion coefficients which determine
the monodromy properties of the conformal blocks.Comment: 18 pages; v2: minor change
Are there really any AdS_2 branes in the euclidean (or not) AdS_3?
We do not find any AdS_2 branes, neither in the H_3^+ WZNW model nor the SL(2,R) WZNW model. We then reexamine the case of the branes that possess a su(2) symmetry: we speculate that they would have to live on the boundary of AdS_3. This cannot be realized in an euclidean spacetime, but in the SL(2,R) WZNW model by analytical continuation
Branes in the Euclidean AdS_3
In this work we propose an exact microscopic description of maximally symmetric branes in a Euclidean background. As shown by Bachas and Petropoulos, the most important such branes are localized along a Euclidean . We provide explicit formulas for the coupling of closed strings to such branes (boundary states) and for the spectral density of open strings. The latter is computed in two different ways first in terms of the open string reflection amplitude and then also from the boundary states by world-sheet duality. This gives rise to an important Cardy type consistency check. All the results are compared in detail with the geometrical picture. We also discuss a second class of branes with spherical symmetry and finally comment on some implications for D-branes in a 2D back hole geometry
Liouville Field Theory on an Unoriented Surface
Liouville field theory on an unoriented surface is investigated, in
particular, the one point function on a RP^2 is calculated. The constraint of
the one point function is obtained by using the crossing symmetry of the two
point function. There are many solutions of the constraint and we can choose
one of them by considering the modular bootstrap.Comment: 13 pages, no figures, LaTeX, minor changes, equations in section 4
are correcte
Continuously Crossing u=z in the H3+ Boundary CFT
For AdS boundary conditions, we give a solution of the H3+ two point function
involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the
full (u,z) unit square. It consists of two patches, one for z<u and one for
u<z. Along the u=z "singularity", the solutions from both patches are shown to
have finite limits and are merged continuously as suggested by the work of
Hosomichi and Ribault. From this two point function, we can derive
b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as
continuous AdS_2 branes are consistent with our novel shift equations without
any new restrictions.Comment: version to appear in JHEP - 12 pages now; sign error with impact on
some parts of the interpretation fixed; material added to become more
self-contained; role of bulk-boundary OPE in section 4 more carefully
discussed; 3 references adde
New Branes and Boundary States
We examine D-branes on , and find a three-brane wrapping the entire
, in addition to 1-branes and instantonic 2-branes previously discussed
in the literature. The three-brane is found using a construction of Maldacena,
Moore, and Seiberg. We show that all these branes satisfy Cardy's condition and
extract the open string spectrum on them.Comment: 18 pages, late
Open String Creation by S-Branes
An sp-brane can be viewed as the creation and decay of an unstable
D(p+1)-brane. It is argued that the decaying half of an sp-brane can be
described by a variant of boundary Liouville theory. The pair creation of open
strings by a decaying s-brane is studied in the minisuperspace approximation to
the Liouville theory. In this approximation a Hagedorn-like divergence is found
in the pair creation rate, suggesting the s-brane energy is rapidly transferred
into closed string radiation.Comment: Talk presented at the Hangzhou String 2002 Conference, August 12-1
On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
We review both the construction of conformal blocks in quantum Liouville
theory and the quantization of Teichm\"uller spaces as developed by Kashaev,
Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert
space acted on by a representation of the mapping class group. According to a
conjecture of H. Verlinde, the two are equivalent. We describe some key steps
in the verification of this conjecture.Comment: Contribution to the proceedings of the 6th International Conference
on CFTs and Integrable Models, Chernogolovka, Russia, September 2002; v2:
Typos corrected, typographical change
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