Suresh Govindarajan

Bio: Suresh Govindarajan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Superpotential & Siegel modular form. The author has an hindex of 21, co-authored 130 publications receiving 1500 citations. Previous affiliations of Suresh Govindarajan include University of Pennsylvania & Indian Institutes of Technology.

Orientifolds of type IIA strings on Calabi-Yau manifolds

Abstract: We identify type IIA orientifolds that are dual to M-theory compactifications on manifolds with G_2-holonomy. We then discuss the construction of crosscap states in Gepner models. (Based on a talk presented by S.G. at PASCOS 2003 held at the Tata Institute of Fundamental Research, Mumbai during Jan. 3-8, 2003.)

Boundary Fermions, Coherent Sheaves and D-branes on Calabi-Yau manifolds

Abstract: We construct boundary conditions in the gauged linear sigma model for B-type D-branes on Calabi-Yau manifolds that correspond to coherent sheaves given by the cohomology of a monad. This necessarily involves the introduction of boundary fields, and in particular, boundary fermions. The large-volume monodromy for these D-brane configurations is implemented by the introduction of boundary contact terms. We also discuss the construction of D-branes associated to coherent sheaves that are the cohomology of complexes of arbitrary length. We illustrate the construction using examples, specifically those associated with the large-volume analogues of the Recknagel-Schomerus states with no moduli. Using some of these examples we also construct D-brane states that arise as bound states of the above rigid configurations and show how moduli can be counted in these cases.

Aquifer heterogeneity on well capture zone and solute transport: numerical investigations with spatial moment analysis

Abstract: The influence of hydraulic conductivity on the movement of flow and nonreactive solute transport through aquifers was evaluated. Several different log-normal probability distribution functions bounded within a fixed range were adopted for simulating the heterogeneous spatial distribution of hydraulic conductivity. Programming codes for two-dimensional confined aquifers were developed to solve the groundwater flow and solute transport equations for a hypothetical setup. Well capture zones were delineated using capture fractions and calculated the concentration moments. Results indicated that an increased shape parameter leads to more heterogeneity in the hydraulic conductivity field and significantly enhances the non-uniformity in the flow and solute plume movements. The findings were generalized for the continuous, discrete, and mixed zonal models, simulated with different parameter values, to yield a lower and upper range for the model derivatives. The results also described the influence of the connectedness of hydraulic conductivity fields on groundwater flow and transport, using capture fractions and plume moments as connectivity indicators. Hence, capture fractions and plume moment statistics aided the careful characterization of aquifer conductivity as a reasonable method of ranking flow and transport connectivity in aquifer flow and transport processes.

Higher dimensional uniformisation and W-geometry

Abstract: We formulate the uniformisation problem underlying the geometry of W_n-gravity using the differential equation approach to W-algebras. We construct W_n-space (analogous to superspace in supersymmetry) as an (n-1) dimensional complex manifold using isomonodromic deformations of linear differential equations. The W_n-manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n,R) which acts properly discontinuously on a simply connected domain in CP^{n-1}. The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W-diffeomorphisms to (linear) diffeomorphisms on the W_n-manifold. We discuss how the Teichmuller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the W_n-manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all ``generic'' W-algebras.

The Topological Vertex

Abstract: 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.

Moduli spaces of local systems and higher Teichmüller theory

Abstract: 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.

The statistics of string/M theory vacua

Abstract: 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.