63 research outputs found
Irregular singularities in Liouville theory
Motivated by problems arising in the study of N=2 supersymmetric gauge
theories we introduce and study irregular singularities in two-dimensional
conformal field theory, here Liouville theory. Irregular singularities are
associated to representations of the Virasoro algebra in which a subset of the
annihilation part of the algebra act diagonally. In this paper we define
natural bases for the space of conformal blocks in the presence of irregular
singularities, describe how to calculate their series expansions, and how such
conformal blocks can be constructed by some delicate limiting procedure from
ordinary conformal blocks. This leads us to a proposal for the structure
functions appearing in the decomposition of physical correlation functions with
irregular singularities into conformal blocks. Taken together, we get a precise
prediction for the partition functions of some Argyres-Douglas type theories on
the four-sphere.Comment: 84 pages, 6 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
c=1 Matrix Models: Equivalences and Open-Closed String Duality
We give an explicit demonstration of the equivalence between the Normal
Matrix Model (NMM) of c=1 string theory at selfdual radius and the
Kontsevich-Penner (KP) model for the same string theory. We relate macroscopic
loop expectation values in the NMM to condensates of the closed string tachyon,
and discuss the implications for open-closed duality. As in c<1, the
Kontsevich-Miwa transform between the parameters of the two theories appears to
encode open-closed string duality, though our results also exhibit some
interesting differences with the c<1 case. We also briefly comment on two
different ways in which the Kontsevich model originates.Comment: 27 pages, latex, 1 figure, typos, discussion added, acknowledgements
update
Loop and surface operators in N=2 gauge theory and Liouville modular geometry
Recently, a duality between Liouville theory and four dimensional N=2 gauge
theory has been uncovered by some of the authors. We consider the role of
extended objects in gauge theory, surface operators and line operators, under
this correspondence. We map such objects to specific operators in Liouville
theory. We employ this connection to compute the expectation value of general
supersymmetric 't Hooft-Wilson line operators in a variety of N=2 gauge
theories.Comment: 60 pages, 11 figures; v3: further minor corrections, published
versio
Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
We study open strings in the noncritical bosonic string theory
compactified on a circle at self-dual radius. These strings live on D-branes
that are extended along the Liouville direction ({\it FZZT} branes). We present
explicit expressions for the disc two- and three-point functions of boundary
operators in this theory, as well as the bulk-boundary two-point function. The
expressions obtained are divergent because of resonant behaviour at self-dual
radius. However, these can be regularised and renormalized in a precise way to
get finite results. The boundary correlators are found to depend only on the
differences of boundary cosmological constants, suggesting a fermionic
behaviour. We initiate a study of the open-string field theory localised to the
physical states, which leads to an interesting matrix model.Comment: 29 pages, harvma
Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings
The target space of minimal strings is embedded into the
phase space of an associated integrable classical mechanical model. This map is
derived from the matrix model representation of minimal strings. Quantum
effects on the target space are obtained from the semiclassical mechanics in
phase space as described by the Wigner function. In the classical limit the
target space is a fold catastrophe of the Wigner function that is smoothed out
by quantum effects. Double scaling limit is obtained by resolving the
singularity of the Wigner function. The quantization rules for backgrounds with
ZZ branes are also derived.Comment: 16 pages, 6 figure
Open/Closed String Duality for Topological Gravity with Matter
The exact FZZT brane partition function for topological gravity with matter
is computed using the dual two-matrix model. We show how the effective theory
of open strings on a stack of FZZT branes is described by the generalized
Kontsevich matrix integral, extending the earlier result for pure topological
gravity. Using the well-known relation between the Kontsevich integral and a
certain shift in the closed-string background, we conclude that these models
exhibit open/closed string duality explicitly. Just as in pure topological
gravity, the unphysical sheets of the classical FZZT moduli space are
eliminated in the exact answer. Instead, they contribute small, nonperturbative
corrections to the exact answer through Stokes' phenomenon.Comment: 23 pages, 1 figure, harvma
A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
We argue that topological matrix models (matrix models of the Kontsevich
type) are examples of exact open/closed duality. The duality works at finite N
and for generic `t Hooft couplings. We consider in detail the paradigm of the
Kontsevich model for two-dimensional topological gravity. We demonstrate that
the Kontsevich model arises by topological localization of cubic open string
field theory on N stable branes. Our analysis is based on standard worldsheet
methods in the context of non-critical bosonic string theory. The stable branes
have Neumann (FZZT) boundary conditions in the Liouville direction. Several
generalizations are possible.Comment: v2: References added; a new section with generalization to non-zero
bulk cosmological constant; expanded discussion on topological localization;
added some comment
Open/closed duality for FZZT branes in c=1
We describe how the matrix integral of Imbimbo and Mukhi arises from a limit
of the FZZT partition function in the double-scaled c=1 matrix model. We show a
similar result for 0A and comment on subtleties in 0B.Comment: 26 pages, 2 figure
Supermatrix models and multi ZZ-brane partition functions in minimal superstring theories
We study (p,q)=(2,4k) minimal superstrings within the minimal superstring
field theory constructed in hep-th/0611045. We explicitly give a solution to
the W_{1+\infty} constraints by using charged D-instanton operators, and show
that the (m,n)-instanton sector with m positive-charged and n negative-charged
ZZ-branes is described by an (m+n)\times (m+n) supermatrix model. We argue that
the supermatrix model can be regarded as an open string field theory on the
multi ZZ-brane system.Comment: 15 pages, 1 figure, minor chang
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