424 research outputs found
Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory
New loop equations for all genera in non-critical string
theory are constructed. Our loop equations include two types of loops, loops
with all Ising spins up (+ loops) and those with all spins down ( loops).
The loop equations generate an algebra which is a certain extension of
algebra and are equivalent to the constraints derived before in the
matrix-model formulation of 2d gravity. Application of these loop equations to
construction of Hamiltonian for string field theory is
considered.Comment: 21 pages, LaTex file, no figure
Loop models, random matrices and planar algebras
We define matrix models that converge to the generating functions of a wide
variety of loop models with fugacity taken in sets with an accumulation point.
The latter can also be seen as moments of a non-commutative law on a subfactor
planar algebra. We apply this construction to compute the generating functions
of the Potts model on a random planar map
Complex Curve of the Two Matrix Model and its Tau-function
We study the hermitean and normal two matrix models in planar approximation
for an arbitrary number of eigenvalue supports. Its planar graph interpretation
is given. The study reveals a general structure of the underlying analytic
complex curve, different from the hyperelliptic curve of the one matrix model.
The matrix model quantities are expressed through the periods of meromorphic
generating differential on this curve and the partition function of the
multiple support solution, as a function of filling numbers and coefficients of
the matrix potential, is shown to be the quasiclassical tau-function. The
relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed.
A general class of solvable multimatrix models with tree-like interactions is
considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of
J.Phys. A on Random Matrix Theor
Analytic Study for the String Theory Landscapes via Matrix Models
We demonstrate a first-principle analysis of the string theory landscapes in
the framework of non-critical string/matrix models. In particular, we discuss
non-perturbative instability, decay rate and the true vacuum of perturbative
string theories. As a simple example, we argue that the perturbative string
vacuum of pure gravity is stable; but that of Yang-Lee edge singularity is
inescapably a false vacuum. Surprisingly, most of perturbative minimal string
vacua are unstable, and their true vacuum mostly does not suffer from
non-perturbative ambiguity. Importantly, we observe that the instability of
these tachyon-less closed string theories is caused by ghost D-instantons (or
ghost ZZ-branes), the existence of which is determined only by non-perturbative
completion of string theory.Comment: v1: 5 pages, 2 figures; v2: references and footnote added; v3: 7
pages, 4 figures, organization changed, explanations expanded, references
added, reconstruction program from arbitrary spectral curves shown explicitl
Kepler-413b: a slightly misaligned, Neptune-size transiting circumbinary planet
We report the discovery of a transiting, Rp = 4.347+/-0.099REarth,
circumbinary planet (CBP) orbiting the Kepler K+M Eclipsing Binary (EB) system
KIC 12351927 (Kepler-413) every ~66 days on an eccentric orbit with ap =
0.355+/-0.002AU, ep = 0.118+/-0.002. The two stars, with MA =
0.820+/-0.015MSun, RA = 0.776+/-0.009RSun and MB = 0.542+/-0.008MSun, RB =
0.484+/-0.024RSun respectively revolve around each other every
10.11615+/-0.00001 days on a nearly circular (eEB = 0.037+/-0.002) orbit. The
orbital plane of the EB is slightly inclined to the line of sight (iEB =
87.33+/-0.06 degrees) while that of the planet is inclined by ~2.5 degrees to
the binary plane at the reference epoch. Orbital precession with a period of
~11 years causes the inclination of the latter to the sky plane to continuously
change. As a result, the planet often fails to transit the primary star at
inferior conjunction, causing stretches of hundreds of days with no transits
(corresponding to multiple planetary orbital periods). We predict that the next
transit will not occur until 2020. The orbital configuration of the system
places the planet slightly closer to its host stars than the inner edge of the
extended habitable zone. Additionally, the orbital configuration of the system
is such that the CBP may experience Cassini-States dynamics under the influence
of the EB, in which the planet's obliquity precesses with a rate comparable to
its orbital precession. Depending on the angular precession frequency of the
CBP, it could potentially undergo obliquity fluctuations of dozens of degrees
(and complex seasonal cycles) on precession timescales.Comment: 48 pages, 13 figure
Continuum Annulus Amplitude from the Two-Matrix Model
An explicit expression for continuum annulus amplitudes having boundary
lengths and is obtained from the two-matrix model for the
case of the unitary series; . In the limit of vanishing
cosmological constant, we find an integral representation of these amplitudes
which is reproduced, for the cases of the and the , by a continuum approach consisting of quantum mechanics of loops
and a matter system integrated over the modular parameter of the annulus. We
comment on a possible relation to the unconventional branch of the Liouville
gravity.Comment: 9 pages, OU-HET 190, revised version. A part of the conclusions has
been corrected. A new result on integral representation of the annulus
amplitudes has been adde
Matrix eigenvalue model: Feynman graph technique for all genera
We present the diagrammatic technique for calculating the free energy of the
matrix eigenvalue model (the model with arbitrary power by the
Vandermonde determinant) to all orders of 1/N expansion in the case where the
limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint
intervals (curves).Comment: Latex, 27 page
Holomorphic matrix models
This is a study of holomorphic matrix models, the matrix models which
underlie the conjecture of Dijkgraaf and Vafa. I first give a systematic
description of the holomorphic one-matrix model. After discussing its
convergence sectors, I show that certain puzzles related to its perturbative
expansion admit a simple resolution in the holomorphic set-up. Constructing a
`complex' microcanonical ensemble, I check that the basic requirements of the
conjecture (in particular, the special geometry relations involving chemical
potentials) hold in the absence of the hermicity constraint. I also show that
planar solutions of the holomorphic model probe the entire moduli space of the
associated algebraic curve. Finally, I give a brief discussion of holomorphic
models, focusing on the example of the quiver, for which I extract
explicitly the relevant Riemann surface. In this case, use of the holomorphic
model is crucial, since the Hermitian approach and its attending regularization
would lead to a singular algebraic curve, thus contradicting the requirements
of the conjecture. In particular, I show how an appropriate regularization of
the holomorphic model produces the desired smooth Riemann surface in the
limit when the regulator is removed, and that this limit can be described as a
statistical ensemble of `reduced' holomorphic models.Comment: 45 pages, reference adde
Extended Seiberg-Witten Theory and Integrable Hierarchy
The prepotential of the effective N=2 super-Yang-Mills theory perturbed in
the ultraviolet by the descendents of the single-trace chiral operators is
shown to be a particular tau-function of the quasiclassical Toda hierarchy. In
the case of noncommutative U(1) theory (or U(N) theory with 2N-2 fundamental
hypermultiplets at the appropriate locus of the moduli space of vacua) or a
theory on a single fractional D3 brane at the ADE singularity the hierarchy is
the dispersionless Toda chain. We present its explicit solutions. Our results
generalize the limit shape analysis of Logan-Schepp and Vershik-Kerov, support
the prior work hep-th/0302191 which established the equivalence of these N=2
theories with the topological A string on CP^1 and clarify the origin of the
Eguchi-Yang matrix integral. In the higher rank case we find an appropriate
variant of the quasiclassical tau-function, show how the Seiberg-Witten curve
is deformed by Toda flows, and fix the contact term ambiguity.Comment: 49 page
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