290 research outputs found
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
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
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
The complex geometry of holographic flows of quiver gauge theories
We argue that the complete Klebanov-Witten flow solution must be described by
a Calabi-Yau metric on the conifold, interpolating between the orbifold at
infinity and the cone over T^(1,1) in the interior. We show that the complete
flow solution is characterized completely by a single, simple, quasi-linear,
second order PDE, or "master equation," in two variables. We show that the
Pilch-Warner flow solution is almost Calabi-Yau: It has a complex structure, a
hermitian metric, and a holomorphic (3,0)-form that is a square root of the
volume form. It is, however, not Kahler. We discuss the relationship between
the master equation derived here for Calabi-Yau geometries and such equations
encountered elsewhere and that govern supersymmetric backgrounds with multiple,
independent fluxes.Comment: 26 pages, harvmac + amssy
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
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
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
Generalized Kaehler Potentials from Supergravity
We consider supersymmetric N=2 solutions with non-vanishing NS three-form.
Building on worldsheet results, we reduce the problem to a single generalized
Monge-Ampere equation on the generalized Kaehler potential K recently
interpreted geometrically by Lindstrom, Rocek, Von Unge and Zabzine. One input
in the procedure is a holomorphic function w that can be thought of as the
effective superpotential for a D3 brane probe. The procedure is hence likely to
be useful for finding gravity duals to field theories with non-vanishing
abelian superpotential, such as Leigh-Strassler theories. We indeed show that a
purely NS precursor of the Lunin-Maldacena dual to the beta-deformed N=4
super-Yang-Mills falls in our class.Comment: "38 pages. v3: improved exposition and minor mistakes corrected in
sec. 4
Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications
Non-perturbative corrections and modular properties of four-dimensional type
IIB Calabi-Yau orientifolds are discussed. It is shown that certain
non-perturbative alpha' corrections survive in the large volume limit of the
orientifold and periodically correct the Kahler potential. These corrections
depend on the NS-NS two form and have to be completed by D-instanton
contributions to transform covariantely under symmetries of the type IIB
orientifold background. It is shown that generically also the D-instanton
superpotential depends on the two-form moduli as well as on the complex
dilaton. These contributions can arise through theta-functions with the dilaton
as modular parameter. An orientifold of the Enriques Calabi-Yau allows to
illustrate these general considerations. It is shown that this compactification
leads to a controlled four-dimensional N=1 effective theory due to the absence
of various quantum corrections. Making contact to the underlying topological
string theory the D-instanton superpotential is proposed to be related to a
specific modular form counting D3, D1, D(-1) degeneracies on the Enriques
Calabi-Yau.Comment: 35 page
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