531 research outputs found
Large N Duality, Lens Spaces and the Chern-Simons Matrix Model
We demonsrate that the spectral curve of the matrix model for Chern-Simons
theory on the Lens space S^{3}/\ZZ_p is precisely the Riemann surface which
appears in the mirror to the blownup, orbifolded conifold. This provides the
first check of the -model large duality for T^{*}(S^{3}/\ZZ_p), p>2.Comment: 12 pages, 2 figure
Bubbling Calabi-Yau geometry from matrix models
We study bubbling geometry in topological string theory. Specifically, we
analyse Chern-Simons theory on both the 3-sphere and lens spaces in the
presence of a Wilson loop insertion of an arbitrary representation. For each of
these three manifolds we formulate a multi-matrix model whose partition
function is the vev of the Wilson loop and compute the spectral curve. This
spectral curve is the reduction to two dimensions of the mirror to a Calabi-Yau
threefold which is the gravitational dual of the Wilson loop insertion. For
lens spaces the dual geometries are new. We comment on a similar matrix model
which appears in the context of Wilson loops in AdS/CFT.Comment: 30 pages; v.2 reference added, minor correction
The Spectral Curve of the Lens Space Matrix Model
Following hep-th/0211098 we study the matrix model which describes the
topological A-model on T^{*}(S^{3}/\ZZ_p). We show that the resolvent has
square root branch cuts and it follows that this is a p cut single matrix
model. We solve for the resolvent and find the spectral curve. We comment on
how this is related to large N transitions and mirror symmetry.Comment: 25 pages, 2 figures, typos corrected, comments adde
Exact Results in ABJM Theory from Topological Strings
Recently, Kapustin, Willett and Yaakov have found, by using localization
techniques, that vacuum expectation values of Wilson loops in ABJM theory can
be calculated with a matrix model. We show that this matrix model is closely
related to Chern-Simons theory on a lens space with a gauge supergroup. This
theory has a topological string large N dual, and this makes possible to solve
the matrix model exactly in the large N expansion. In particular, we find the
exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in
the ABJM theory, as a function of the 't Hooft parameters, and in the planar
limit. This expression gives an exact interpolating function between the weak
and the strong coupling regimes. The behavior at strong coupling is in precise
agreement with the prediction of the AdS string dual. We also give explicit
results for the 1/2 BPS Wilson loop recently constructed by Drukker and
TrancanelliComment: 18 pages, two figures, small misprints corrected and references
added, final version to appear in JHE
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
We develop techniques to compute multi-instanton corrections to the 1/N
expansion in matrix models described by orthogonal polynomials. These
techniques are based on finding trans-series solutions, i.e. formal solutions
with exponentially small corrections, to the recursion relations characterizing
the free energy. We illustrate this method in the Hermitian, quartic matrix
model, and we provide a detailed description of the instanton corrections in
the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel
resummation techniques and results from the theory of resurgent functions to
relate the formal multi-instanton series to the nonperturbative definition of
the matrix model. We study this relation in the case of the GWW model and its
double-scaling limit, providing in this way a nice illustration of various
mechanisms connecting the resummation of perturbative series to nonperturbative
results, like the cancellation of nonperturbative ambiguities. Finally, we
argue that trans-series solutions are also relevant in the context of
topological string theory. In particular, we point out that in topological
string models with both a matrix model and a large N gauge theory description,
the nonperturbative, holographic definition involves a sum over the
multi-instanton sectors of the matrix modelComment: 50 pages, 12 figures, comments and references added, small
correction
Wall-crossing, open BPS counting and matrix models
We consider wall-crossing phenomena associated to the counting of D2-branes
attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both
from M-theory and matrix model perspective. Firstly, from M-theory viewpoint,
we review that open BPS generating functions in various chambers are given by a
restriction of the modulus square of the open topological string partition
functions. Secondly, we show that these BPS generating functions can be
identified with integrands of matrix models, which naturally arise in the free
fermion formulation of corresponding crystal models. A parameter specifying a
choice of an open BPS chamber has a natural, geometric interpretation in the
crystal model. These results extend previously known relations between open
topological string amplitudes and matrix models to include chamber dependence.Comment: 25 pages, 8 figures, published versio
Inferior vestibular neuritis: 3 cases with clinical features of acute vestibular neuritis, normal calorics but indications of saccular failure
BACKGROUND: Vestibular neuritis (VN) is commonly diagnosed by demonstration of unilateral vestibular failure, as unilateral loss of caloric response. As this test reflects the function of the superior part of the vestibular nerve only, cases of pure inferior nerve neuritis will be lost. CASE PRESENTATIONS: We describe three patients with symptoms suggestive of VN, but normal calorics. All 3 had unilateral loss of vestibular evoked myogenic potential. A slight, asymptomatic position dependent nystagmus, with the pathological ear down, was observed. CONCLUSION: We believe that these patients suffer from pure inferior nerve vestibular neuritis
Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
We study various aspects of the matrix models calculating free energies and
Wilson loop observables in supersymmetric Chern-Simons-matter theories on the
three-sphere. We first develop techniques to extract strong coupling results
directly from the spectral curve describing the large N master field. We show
that the strong coupling limit of the gauge theory corresponds to the so-called
tropical limit of the spectral curve. In this limit, the curve degenerates to a
planar graph, and matrix model calculations reduce to elementary line integrals
along the graph. As an important physical application of these tropical
techniques, we study N=3 theories with fundamental matter, both in the quenched
and in the unquenched regimes. We calculate the exact spectral curve in the
Veneziano limit, and we evaluate the planar free energy and Wilson loop
observables at strong coupling by using tropical geometry. The results are in
agreement with the predictions of the AdS duals involving tri-Sasakian
manifoldsComment: 32 pages, 7 figures. v2: small corrections, added an Appendix on the
relation with the approach of 1011.5487. v3: further corrections and
clarifications, final version to appear in JHE
On The Inflaton Potential From Antibranes in Warped Throats
We compute the force between a stack of smeared antibranes at the bottom of a
warped throat and a stack of smeared branes at some distance up the throat,
both for anti-D3 branes and for anti-M2 branes. We perform this calculation in
two ways: first, by treating the antibranes as probes in the background sourced
by the branes and second, by treating the branes as probes in the candidate
background sourced by the antibranes. These two very different calculations
yield exactly the same expression for the force, for all values of the
brane-antibrane separation. This indicates that the force between a brane and
an antibrane is not screened in backgrounds where there is positive charge
dissolved in flux, and gives a way to precisely compute the inflaton potential
in certain string cosmology scenarios.Comment: 9 page
The general (2,2) gauged sigma model with three--form flux
We find the conditions under which a Riemannian manifold equipped with a
closed three-form and a vector field define an on--shell N=(2,2) supersymmetric
gauged sigma model. The conditions are that the manifold admits a twisted
generalized Kaehler structure, that the vector field preserves this structure,
and that a so--called generalized moment map exists for it. By a theorem in
generalized complex geometry, these conditions imply that the quotient is again
a twisted generalized Kaehler manifold; this is in perfect agreement with
expectations from the renormalization group flow. This method can produce new
N=(2,2) models with NS flux, extending the usual Kaehler quotient construction
based on Kaehler gauged sigma models.Comment: 24 pages. v2: typos fixed, other minor correction
- …