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

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

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

Loop operators and S-duality from curves on Riemann surfaces

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.Comment: 41 page

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

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

On N = 2 Truncations of IIB on T^{1,1}

We study the N=4 gauged supergravity theory which arises from the consistent truncation of IIB supergravity on the coset T^{1,1}. We analyze three N=2 subsectors and in particular we clarify the relationship between true superpotentials for gauged supergravity and certain fake superpotentials which have been widely used in the literature. We derive a superpotential for the general reduction of type I supergravity on T^{1,1} and this together with a certain solution generating symmetry is tantamount to a superpotential for the baryonic branch of the Klebanov-Strassler solution.Comment: 32 pages, v2:references adde