qq-Stability conditions via qq-quadratic differentials for Calabi-Yau-X\mathbb{X} categories

We construct a quiver with superpotential $(Q_\mathbf{T},W_\mathbf{T})$ from a marked surface $\mathbf{S}$ with full formal arc system $\mathbf{T}$. Categorically, we show that the associated cluster-$\mathbb{X}$ category is Haiden-Katzarkov-Kontsevich's topological Fukaya category $\mathcal{D}_{\infty}(\mathbf{T})$ of $\mathbf{S}$, which is also an $\mathbb{X}$-baric heart of the Calabi-Yau-$\mathbb{X}$ category $\mathcal{D}_{\mathbb{X}}(\mathbf{T})$ of $(Q_\mathbf{T},W_\mathbf{T})$. Thus stability conditions on $\mathcal{D}_{\infty}(\mathbf{T})$ induces $q$-stability conditions on $\mathcal{D}_{\mathbb{X}}(\mathbf{T})$. Geometrically, we identify the space of $q$-quadratic differentials on the logarithm surface $\log\mathbf{S}_\Delta$, with the space of induced $q$-stability conditions on $\mathcal{D}_{\mathbb{X}}(\mathbf{T})$, with a complex parameter $s$ satisfying $\operatorname{Re}(s)\gg1$. When $s=N$ is an integer, the result gives an $N$-analogue of Bridgeland-Smith's result for realizing stability conditions on the orbit Calabi-Yau-$N$ category $\mathcal{D}_{\mathbb{X}}(\mathbf{T})\mathbin{/\mkern-6mu/}[\mathbb{X}-N]$

The many faces of brane-flux annihilation

Fluxes can decay via the nucleation of Brown-Teitelboim bubbles, but when the decaying fluxes induce D-brane charges this process must be accompanied with an annihilation of D-branes. This occurs via dynamics inside the bubble wall as was well described for (anti-)D3 branes branes annihilating against 3-form fluxes. In this paper we extend this to the other Dp branes with p smaller than seven. Generically there are two decay channels: one for the RR flux and one for the NSNS flux. The RR channel is accompanied by brane annihilation that can be understood from the Dp branes polarising into D(p+2) branes, whereas the NSNS channel corresponds to Dp branes polarising into NS5 branes or KK5 branes. We illustrate this with the decay of antibranes probing local toroidal throat geometries obtained from T-duality of the D6 solution in massive type IIA. We show that anti-Dp branes are metastable against annihilation in these backgrounds, at least at the probe level.Comment: 23 pages, 7 figure

Hyperkahler manifolds and nonabelian Hodge theory of (irregular) curves

Short survey based on talk given at the Institut Henri Poincare January 17th 2012, during program on surface groups. The aim was to describe some background results before describing in detail (in subsequent talks) the results of [Boa11c] related to wild character varieties and irregular mapping class groups.Comment: 16 pages, 2 figures, 3 table

An example of the Langlands correspondence for irregular rank two connections on P^1

Special kinds of rank 2 vector bundles with (possibly irregular) connections on P^1 are considered. We construct an equivalence between the derived category of quasi-coherent sheaves on the moduli stack of such bundles and the derived category of modules over a TDO ring on certain non-separated curve. We identify this curve with the coarse moduli space of some parabolic bundles on P^1. Then our equivalence becomes an example of the categorical Langlands correspondence.Comment: Section 5 was shortened by referring to results of Hernandez Ruiperez et al. The reader might want to look at the previous (2nd) version for a more self-contained exposition. Other minor change

Gauge Theory, Ramification, And The Geometric Langlands Program

In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of ``surface operators,'' which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on curves. We describe the relevant surface operators in N=4 super Yang-Mills theory, and the parameters they depend on, and analyze how S-duality acts on these parameters. Then, after compactifying on a Riemann surface, we show that the hypothesis of S-duality for surface operators leads to a natural extension of the geometric Langlands program for the case of tame ramification. The construction involves an action of the affine Weyl group on the cohomology of the moduli space of Higgs bundles with ramification, and an action of the affine braid group on A-branes or B-branes on this space.Comment: 160 p

Classical and quantum temperature fluctuations via holography

We study local temperature fluctuations in a 2+1 dimensional CFT on the sphere, dual to a black hole in asymptotically AdS spacetime. The fluctuation spectrum is governed by the lowest-lying hydrodynamic modes of the system whose frequency and damping rate determine whether temperature fluctuations are thermal or quantum. We calculate numerically the corresponding quasinormal frequencies and match the result with the hydrodynamics of the dual CFT at large temperature. As a by-product of our analysis we determine the appropriate boundary conditions for calculating low-lying quasinormal modes for a four-dimensional Reissner-Nordstr\"om black hole in global AdS.Comment: LaTeX: 31 pages, 7 figures; V2: reference added; V3: added/updated charged cas

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde

Frobenius manifold structures on the spaces of abelian integrals

Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use D-modules, deformation theory, and homological algebra to give a coordinate-free description of these structures. It turns out that the tangent sheaf multiplication has a cohomological origin, while the Levi-Civita connection is related to 1-dimensional isomonodromic deformations.Comment: Expanded version. The case of an abelian integral with multiple poles is treated. Other minor improvements. Final versio