237 research outputs found
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
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
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
A lecture on the Liouville vertex operators
We reconsider the construction of exponential fields in the quantized
Liouville theory. It is based on a free-field construction of a continuous
family or chiral vertex operators. We derive the fusion and braid relations of
the chiral vertex operators. This allows us to simplify the verification of
locality and crossing symmetry of the exponential fields considerably. The
calculation of the matrix elements of the exponential fields leads to a
constructive derivation of the formula proposed by Dorn/Otto and the brothers
Zamolodchikov.Comment: Contribution to the proceedings of the 6th International Conference
on CFTs and Integrable Models, Chernogolovka, Russia, 2002 v2: Remarks added,
typos correcte
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 crossing relation in the presence of defects
The OPE of local operators in the presence of defect lines is considered both
in the rational CFT and the Virasoro (Liouville) theory. The duality
transformation of the 4-point function with inserted defect operators is
explicitly computed. The two channels of the correlator reproduce the
expectation values of the Wilson and 't Hooft operators, recently discussed in
Liouville theory in relation to the AGT conjecture.Comment: TEX file with harvmac; v3: JHEP versio
Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
A four point function of basic Neveu-Schwarz exponential fields is
constructed in the N = 1 supersymmetric Liouville field theory. Although the
basic NS structure constants were known previously, we present a new
derivation, based on a singular vector decoupling in the NS sector. This allows
to stay completely inside the NS sector of the space of states, without
referencing to the Ramond fields. The four-point construction involves also the
NS blocks, for which we suggest a new recursion representation, the so-called
elliptic one. The bootstrap conditions for this four point correlation function
are verified numerically for different values of the parameters
N=2 Liouville Theory with Boundary
We study N=2 Liouville theory with arbitrary central charge in the presence
of boundaries. After reviewing the theory on the sphere and deriving some
important structure constants, we investigate the boundary states of the theory
from two approaches, one using the modular transformation property of annulus
amplitudes and the other using the bootstrap of disc two-point functions
containing degenerate bulk operators. The boundary interactions describing the
boundary states are also proposed, based on which the precise correspondence
between boundary states and boundary interactions is obtained. The open string
spectrum between D-branes is studied from the modular bootstrap approach and
also from the reflection relation of boundary operators, providing a
consistency check for the proposal.Comment: 1+48 pages, no figure. typos corrected and references added. the
version to appear in JHE
D-branes in the Euclidean and T-duality
We show that D-branes in the Euclidean can be naturally associated to
the maximally isotropic subgroups of the Lu-Weinstein double of SU(2). This
picture makes very transparent the residual loop group symmetry of the D-brane
configurations and gives also immediately the D-branes shapes and the
-model boundary conditions in the de Sitter T-dual of the
WZW model.Comment: 29 pages, LaTeX, references adde
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