139 research outputs found
Boundary operators in minimal Liouville gravity and matrix models
We interpret the matrix boundaries of the one matrix model (1MM) recently
constructed by two of the authors as an outcome of a relation among FZZT
branes. In the double scaling limit, the 1MM is described by the (2,2p+1)
minimal Liouville gravity. These matrix operators are shown to create a
boundary with matter boundary conditions given by the Cardy states. We also
demonstrate a recursion relation among the matrix disc correlator with two
different boundaries. This construction is then extended to the two matrix
model and the disc correlator with two boundaries is compared with the
Liouville boundary two point functions. In addition, the realization within the
matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page
Boundary changing operators in the O(n) matrix model
We continue the study of boundary operators in the dense O(n) model on the
random lattice. The conformal dimension of boundary operators inserted between
two JS boundaries of different weight is derived from the matrix model
description. Our results are in agreement with the regular lattice findings. A
connection is made between the loop equations in the continuum limit and the
shift relations of boundary Liouville 3-points functions obtained from Boundary
Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve
A note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory
We propose an alternative method to study the saddle point equation in the
strong coupling limit for the Wilson loop in D=4 super
Yang-Mills with an SU(N) gauge group and 2N hypermultiplets. This method is
based on an approximation of the integral equation kernel which allows to solve
the simplified problem exactly. To determine the accuracy of this
approximation, we compare our results to those obtained recently by Passerini
and Zarembo. Although less precise, this simpler approach provides an explicit
expression for the density of eigenvalues that is used to derive the planar
free energy.Comment: 12 pages, v2: section 2.5 (Free Energy) amended and reference added,
to appear in J. Phys.
FZZT Brane Relations in the Presence of Boundary Magnetic Fields
We show how a boundary state different from the (1,1) Cardy state may be
realised in the (m,m+1) minimal string by the introduction of an auxiliary
matrix into the standard two hermitian matrix model. This boundary is a natural
generalisation of the free spin boundary state in the Ising model. The
resolvent for the auxiliary matrix is computed using an extension of the
saddle-point method of Zinn-Justin to the case of non-identical potentials. The
structure of the saddle-point equations result in a Seiberg-Shih like relation
between the boundary states which is valid away from the continuum limit, in
addition to an expression for the spectral curve of the free spin boundary
state. We then show how the technique may be used to analyse boundary states
corresponding to a boundary magnetic field, thereby allowing us to generalise
the work of Carroll et al. on the boundary renormalisation flow of the Ising
model, to any (m,m+1) model.Comment: 23 pages, 5 figures (3 new). Two new sections added giving examples
of the construction. Explanations clarified. Minor changes to the conclusion
but main results unchanged. Matches published versio
Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
We compute the generating functions of a O(n) model (loop gas model) on a
random lattice of any topology. On the disc and the cylinder, they were already
known, and here we compute all the other topologies. We find that the
generating functions (and the correlation functions of the lattice) obey the
topological recursion, as usual in matrix models, i.e they are given by the
symplectic invariants of their spectral curve.Comment: pdflatex, 89 pages, 12 labelled figures (15 figures at all), minor
correction
Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
We study the interactions of Maldacena's long folded strings in
two-dimensional string theory. We find the amplitude for a state containing two
long folded strings to come and go back to infinity. We calculate this
amplitude both in the worldsheet theory and in the dual matrix model, the
Matrix Quantum Mechanics. The matrix model description allows to evaluate the
amplitudes involving any number of long strings, which are given by the mixed
trace correlators in an effective two-matrix model.Comment: 39 pages, 6 figure
Beyond LLM in M-theory
The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent
Killing directions when a general Killing spinor ansatz is considered. Here we
show that these directions always commute, identify when the Killing spinors
are charged, and show that both their inner product and resulting geometry are
governed by two fundamental constants. In particular, setting one constant to
zero leads to AdS7 x S4, setting the other to zero gives AdS4 x S7, while flat
spacetime is recovered when both these constants are zero. Furthermore, when
the constants are equal, the spacetime is either LLM, or it corresponds to the
Kowalski-Glikman solution where the constants are simply the mass parameter.Comment: 1+30 pages, footnote adde
Matrix models for irregular conformal blocks and Argyres-Douglas theories
As regular conformal blocks describe the N=2 superconformal gauge theories in
four dimensions, irregular conformal blocks are expected to reproduce the
instanton partition functions of the Argyres-Douglas theories. In this paper,
we construct matrix models which reproduce the irregular conformal conformal
blocks of the Liouville theory on sphere, by taking a colliding limit of the
Penner-type matrix models. The resulting matrix models have not only
logarithmic terms but also rational terms in the potential. We also discuss
their relation to the Argyres-Douglas type theories.Comment: 42 pages, 2 figures; v2: minor corrections; v3: minor corrections,
added the second paragraph in section
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