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

Worldsheet approaches to D-branes on supersymmetric cycles

D-branes, exceptional sheaves and quivers on Calabi-Yau manifolds: From Mukai to McKay

Human health risk assessment of ground water contaminated with petroleum PAHs using Monte Carlo simulations: A case study of an Indian metropolitan city.

We show that the generating function of electrically charged 1/2-BPS states in N=4 supersymmetric Z_N-CHL orbifolds of the heterotic string on T^6 are given by multiplicative eta-products. The eta-products are determined by the cycle shape of the corresponding symplectic involution in the dual type II picture. This enables us to complete the construction of the genus-two Siegel modular forms due to David, Jatkar and Sen [arXiv:hep-th/0609109] for Z_N orbifolds when N is non-prime. We study the Z_4 CHL orbifold in detail and show that the associated Siegel modular forms, \Phi_3(Z) and \widetilde{\Phi}_3(Z), are given by the square of the product of three even genus-two theta constants. Extending work by us[arXiv:0807.4451] as well as Cheng and Dabholkar[arXiv:0809.4258], we show that their `square roots' appear as the denominator formulae of two distinct Borcherds-Kac-Moody (BKM) Lie superalgebras. The BKM Lie superalgebra associated with the generating function of 1/4-BPS states, i.e., \widetilde{\Phi}_3(Z) has a parabolic root system with a light-like Weyl vector and the walls of its fundamental Weyl chamber are mapped to the walls of marginal stability of the 1/4-BPS states.

BKM Lie superalgebras from dyon spectra in Z_N-CHL orbifolds for composite N

http://cds.cern.ch/record/446639/files/0007075.pdf

Suresh Govindarajan

Papers

Worldsheet approaches to D-branes on supersymmetric cycles

D-branes, exceptional sheaves and quivers on Calabi-Yau manifolds: From Mukai to McKay

Human health risk assessment of ground water contaminated with petroleum PAHs using Monte Carlo simulations: A case study of an Indian metropolitan city.

BKM Lie superalgebras from dyon spectra in Z_N-CHL orbifolds for composite N

On D-branes from gauged linear sigma models