The flow of homogeneous fluids through porous media: analogies with other physical problems

http://cds.cern.ch/record/994225/files/0610327.pdf

Four-dimensional string compactifications with D-branes, orientifolds and fluxes

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

/pdf/the-topological-vertex-3lrad1kwkt.pdf

The Topological Vertex

Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely related to the moduli spaces of G-local systems on S. We show that they carry a lot of interesting structures. In particular we define a distinguished collection of coordinate systems, equivariant under the action of the mapping class group of S. We prove that their transition functions are subtraction free. Thus we have positive structures on these moduli spaces. Therefore we can take their points with values in any positive semifield. Their positive real points provide the two higher Teichmuller spaces related to G and S, while the points with values in the tropical semifields provide the lamination spaces. We define the motivic avatar of the Weil–Petersson form for one of these spaces. It is related to the motivic dilogarithm.

/pdf/moduli-spaces-of-local-systems-and-higher-teichmuller-theory-36h32nsutb.pdf

Moduli spaces of local systems and higher Teichmüller theory

We discuss systematic approaches to the classification of string/M theory vacua, and physical questions this might help us resolve. To this end, we initiate the study of ensembles of effective Lagrangians, which can be used to precisely study the predictive power of string theory, and in simple examples can lead to universality results. Using these ideas, we outline an approach to estimating the number of vacua of string/M theory which can realize the Standard Model.

https://iopscience.iop.org/article/10.1088/1126-6708/2003/05/046/pdf

The statistics of string/M theory vacua

Higher dimensional uniformisation and W-geometry

In this paper we study the relation between parabolic Higgs vector bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those parabolic Higgs bundles that correspond to Fuchsian representations. We also study the Higgs bundles that give representations whose image is contained, after conjugation, in SL(k, R). We compute the real dimension of one of the components of this space of representations, which in the absence of punctures is the generalized Teichmuller space introduced by Hitchin, and which in the case of k = 2 is the usual Teichmuller space of the punctured surface.

/pdf/parabolic-higgs-bundles-and-teichmuller-spaces-for-punctured-fl41zfbddy.pdf

Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces

BKM Lie superalgebras from counting twisted CHL dyons - II

In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those parabolic Higgs bundles that correspond to Fuchsian representations. We also study the Higgs bundles that give representations whose image is contained, after conjugation, in SL($k,\Bbb R$). We compute the real dimension of one of the components of this space of representations, which in the absence of punctures is the generalized Teichm\"uller space introduced by Hitchin, and which in the case of $k=2$ is the Teichm\"uller space of the Riemann surface.

Suresh Govindarajan

Papers

Higher dimensional uniformisation and W-geometry

Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces

BKM Lie superalgebras from counting twisted CHL dyons - II

Parabolic Higgs bundles and Teichm\"uller spaces for punctured surfaces

Chiral Rings and Physical States in c < 1 String Theory