114 research outputs found
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
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
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
Non-Perturbative Topological Strings And Conformal Blocks
We give a non-perturbative completion of a class of closed topological string
theories in terms of building blocks of dual open strings. In the specific case
where the open string is given by a matrix model these blocks correspond to a
choice of integration contour. We then apply this definition to the AGT setup
where the dual matrix model has logarithmic potential and is conjecturally
equivalent to Liouville conformal field theory. By studying the natural
contours of these matrix integrals and their monodromy properties, we propose a
precise map between topological string blocks and Liouville conformal blocks.
Remarkably, this description makes use of the light-cone diagrams of closed
string field theory, where the critical points of the matrix potential
correspond to string interaction points.Comment: 36 page
Penrose limit and string quantization in AdS_3 \times S^3
We consider corrections to the Penrose limit of AdS_3 \times S^3 with NS-NS
flux which are due to the terms next to leading order in inverse radius
expansion. The worldsheet theory of a lightcone string is interacting due to
the presence of quartic terms in the action. Perturbative corrections to the
spectrum are shown to agree with the results from the exact quantization in
AdS_3 \times S^3.Comment: 18 pages v2: typos fixed, reference added, to appear in JHE
Timelike Boundary Liouville Theory
The timelike boundary Liouville (TBL) conformal field theory consisting of a
negative norm boson with an exponential boundary interaction is considered. TBL
and its close cousin, a positive norm boson with a non-hermitian boundary
interaction, arise in the description of the accumulation point of
minimal models, as the worldsheet description of open string tachyon
condensation in string theory and in scaling limits of superconductors with
line defects. Bulk correlators are shown to be exactly soluble. In contrast,
due to OPE singularities near the boundary interaction, the computation of
boundary correlators is a challenging problem which we address but do not fully
solve. Analytic continuation from the known correlators of spatial boundary
Liouville to TBL encounters an infinite accumulation of poles and zeros. A
particular contour prescription is proposed which cancels the poles against the
zeros in the boundary correlator d(\o) of two operators of weight \o^2 and
yields a finite result. A general relation is proposed between two-point CFT
correlators and stringy Bogolubov coefficients, according to which the
magnitude of d(\o) determines the rate of open string pair creation during
tachyon condensation. The rate so obtained agrees at large \o with a
minisuperspace analysis of previous work. It is suggested that the mathematical
ambiguity arising in the prescription for analytic continuation of the
correlators corresponds to the physical ambiguity in the choice of open string
modes and vacua in a time dependent background.Comment: 28 pages, 1 figure, v2 reference and acknowledgement adde
Branes, Rings and Matrix Models in Minimal (Super)string Theory
We study both bosonic and supersymmetric (p,q) minimal models coupled to
Liouville theory using the ground ring and the various branes of the theory.
From the FZZT brane partition function, there emerges a unified, geometric
description of all these theories in terms of an auxiliary Riemann surface
M_{p,q} and the corresponding matrix model. In terms of this geometric
description, both the FZZT and ZZ branes correspond to line integrals of a
certain one-form on M_{p,q}. Moreover, we argue that there are a finite number
of distinct (m,n) ZZ branes, and we show that these ZZ branes are located at
the singularities of M_{p,q}. Finally, we discuss the possibility that the
bosonic and supersymmetric theories with (p,q) odd and relatively prime are
identical, as is suggested by the unified treatment of these models.Comment: 72 pages, 3 figures, improved treatment of FZZT and ZZ branes, minor
change
D-brane Decay in Two-Dimensional String Theory
We consider unstable D0-branes of two dimensional string theory, described by
the boundary state of Zamolodchikov and Zamolodchikov [hep-th/0101152]
multiplied by the Neumann boundary state for the time coordinate . In the
dual description in terms of the matrix model, this D0-brane is described
by a matrix eigenvalue on top of the upside down harmonic oscillator potential.
As suggested by McGreevy and Verlinde [hep-th/0304224], an eigenvalue rolling
down the potential describes D-brane decay. As the eigenvalue moves down the
potential to the asymptotic region it can be described as a free relativistic
fermion. Bosonizing this fermion we get a description of the state in terms of
a coherent state of the tachyon field in the asymptotic region, up to a
non-local linear field redefinition by an energy-dependent phase. This coherent
state agrees with the exponential of the closed string one-point function on a
disk with Sen's marginal boundary interaction for which describes D0-brane
decay.Comment: 19 pages, harvmac, minor change
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