311 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
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
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
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
Holographic Coulomb Branch Flows with N=1 Supersymmetry
We obtain a large, new class of N=1 supersymmetric holographic flow
backgrounds with U(1)^3 symmetry. These solutions correspond to flows toward
the Coulomb branch of the non-trivial N=1 supersymmetric fixed point. The
massless (complex) chiral fields are allowed to develop vevs that are
independent of their two phase angles, and this corresponds to allowing the
brane to spread with arbitrary, U(1)^2 invariant, radial distributions in each
of these directions. Our solutions are "almost Calabi-Yau:" The metric is
hermitian with respect to an integrable complex structure, but is not Kahler.
The "modulus squared" of the holomorphic (3,0)-form is the volume form, and the
complete solution is characterized by a function that must satisfy a single
partial differential equation that is closely related to the Calabi-Yau
condition. The deformation from a standard Calabi-Yau background is driven by a
non-trivial, non-normalizable 3-form flux dual to a fermion mass that reduces
the supersymmetry to N=1. This flux also induces dielectric polarization of the
D3-branes into D5-branes.Comment: 22 pages; harvmac. Typos corrected;small improvements in presentatio
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
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
Supergravity Instabilities of Non-Supersymmetric Quantum Critical Points
Motivated by the recent use of certain consistent truncations of M-theory to
study condensed matter physics using holographic techniques, we study the
SU(3)-invariant sector of four-dimensional, N=8 gauged supergravity and compute
the complete scalar spectrum at each of the five non-trivial critical points.
We demonstrate that the smaller SU(4)^- sector is equivalent to a consistent
truncation studied recently by various authors and find that the critical point
in this sector, which has been proposed as the ground state of a holographic
superconductor, is unstable due to a family of scalars that violate the
Breitenlohner-Freedman bound. We also derive the origin of this instability in
eleven dimensions and comment on the generalization to other embeddings of this
critical point which involve arbitrary Sasaki-Einstein seven manifolds. In the
spirit of a resurging interest in consistent truncations, we present a formal
treatment of the SU(3)-invariant sector as a U(1)xU(1) gauged N=2 supergravity
theory coupled to one hypermultiplet.Comment: 46 page
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