21 research outputs found
Asymmetric Cosets
The aim of this work is to present a general theory of coset models G/H in
which different left and right actions of H on G are gauged. Our main results
include a formula for their modular invariant partition function, the
construction of a large set of boundary states and a general description of the
corresponding brane geometries. The paper concludes with some explicit
applications to the base of the conifold and to the time-dependent Nappi-Witten
background.Comment: 34 pages, LaTeX, 8 figures, 1 table, v2: references added, v3: typos
correcte
Boundary Liouville theory at c=1
The c=1 Liouville theory has received some attention recently as the
Euclidean version of an exact rolling tachyon background. In an earlier paper
it was shown that the bulk theory can be identified with the interacting c=1
limit of unitary minimal models. Here we extend the analysis of the c=1-limit
to the boundary problem. Most importantly, we show that the FZZT branes of
Liouville theory give rise to a new 1-parameter family of boundary theories at
c=1. These models share many features with the boundary Sine-Gordon theory, in
particular they possess an open string spectrum with band-gaps of finite width.
We propose explicit formulas for the boundary 2-point function and for the
bulk-boundary operator product expansion in the c=1 boundary Liouville model.
As a by-product of our analysis we also provide a nice geometric interpretation
for ZZ branes and their relation with FZZT branes in the c=1 theory.Comment: 37 pages, 1 figure. Minor error corrected, slight change in result
(1.6
On Minisuperspace Models of S-branes
In this note we reconsider the minisuperspace toy models for rolling and
bouncing tachyons. We show that the theories require to choose boundary
conditions at infinity since particles in an exponentially unbounded potential
fall to infinity in finite world-sheet time. Using standard techniques from
operator theory, we determine the possible boundary conditions and we compute
the corresponding energy spectra and minisuperspace 3-point functions. Based on
this analysis we argue in particular that world-sheet models of S-branes
possess a discrete spectrum of conformal weights containing both positive and
negative values. Finally, some suggestions are made for possible relations with
previous studies of the minisuperspace theory.Comment: 24 pages, 3 figure
Rolling Tachyons from Liouville theory
In this work we propose an exact solution of the c=1 Liouville model, i.e. of
the world-sheet theory that describes the homogeneous decay of a closed string
tachyon. Our expressions are obtained through careful extrapolation from the
correlators of Liouville theory with c > 25. In the c=1 limit, we find two
different theories which differ by the signature of Liouville field. The
Euclidean limit coincides with the interacting c=1 theory that was constructed
by Runkel and Watts as a limit of unitary minimal models. The couplings for the
Lorentzian limit are new. In contrast to the behavior at c > 1, amplitudes in
both c=1 models are non-analytic in the momenta and consequently they are not
related by Wick rotation.Comment: 22 page
Lectures on Branes in Curved Backgrounds
These lectures provide an introduction to the microscopic description of
branes in curved backgrounds. After a brief reminder of the flat space theory,
the basic principles and techniques of (rational) boundary conformal field
theory are presented in the second lecture. The general formalism is then
illustrated through a detailed discussion of branes on compact group manifolds.
In the final lecture, many more recent developments are reviewed, including
some results for non-compact target spaces.Comment: 109 pages, 11 figures, Lectures presented at the third RTN school on
`The Quantum Structure of Spacetime and the Geometric Nature of Fundamental
Interactions', Utrecht, January 200
Superspace Parafermions
We describe several families of non-unitary coset conformal field theories
that possess truly marginal couplings. These generalize the known examples of
Wess-Zumino-Witten models on supergroups such as PSU(n|n) or OSP(2n+2|2n). Our
extension includes coset space sigma models, affine Toda theories or
Gross-Neveu models which are believed to arise in certain limits.Comment: 4 page
N=2 Superconformal Symmetry in Super Coset Models
We extend the Kazama-Suzuki construction of models with N=(2,2) world-sheet
supersymmetry to cosets S/K of supergroups. Among the admissible target spaces
that allow for an extension to N=2 superconformal algebras are some simple Lie
supergroups, including PSL(N|N). Our general analysis is illustrated at the
example of the N=1 WZNW model on GL(1|1). After constructing its N=2
superconformal algebra we determine the (anti-)chiral ring of the theory. It
exhibits an interesting interplay between world-sheet and target space
supersymmetry.Comment: 7 pages; v2: Typos corrected, three references adde
WZNW Model From Liouville Field Theory.
There exists an intriguing relation between genus zero correlation functions
in the H^+_3 WZNW model and in Liouville field theory. We provide a path
integral derivation of the correspondence and then use our new approach to
generalize the relation to surfaces of arbitrary genus g. In particular we
determine the correlation functions of N primary fields in the WZNW model
explicitly through Liouville correlators with N+2g-2 additional insertions of
certain degenerate fields. The paper concludes with a list of interesting
further extensions and a few comments on the relation to the geometric
Langlands program.Comment: 33 pages, no figure, minor changes, several equations correcte
The FZZ-Duality Conjecture: A Proof
We prove that the cigar conformal field theory is dual to the Sine-Liouville
model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov.
Since both models possess the same chiral algebra, our task is to show that
correlations of all tachyon vertex operators agree. We accomplish this goal
through an off-critical version of the geometric Langlands duality for sl(2).
More explicitly, we combine the well-known self-duality of Liouville theory
with an intriguing correspondence between the cigar and Liouville field theory.
The latter is derived through a path integral treatment. After a very detailed
discussion of genus zero amplitudes, we extend the duality to arbitrary closed
surfaces.Comment: 42 page