On the Landau-Ginzburg description of Boundary CFTs and special Lagrangian submanifolds

We consider Landau-Ginzburg (LG) models with boundary conditions preserving A-type N=2 supersymmetry. We show the equivalence of a linear class of boundary conditions in the LG model to a particular class of boundary states in the corresponding CFT by an explicit computation of the open-string Witten index in the LG model. We extend the linear class of boundary conditions to general non-linear boundary conditions and determine their consistency with A-type N=2 supersymmetry. This enables us to provide a microscopic description of special Lagrangian submanifolds in C^n due to Harvey and Lawson. We generalise this construction to the case of hypersurfaces in P^n. We find that the boundary conditions must necessarily have vanishing Poisson bracket with the combination (W(\phi)-\bar{W}(\bar{\phi})), where W(\phi) is the appropriate superpotential for the hypersurface. An interesting application considered is the T^3 supersymmetric cycle of the quintic in the large complex structure limit.Comment: 28+1 pages; no figures; requires JHEP.cls, amssymb; (v2) typo corrected; (v3) references adde

Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term

We study the nonrelativistic nonlinear sigma model with Hopf term in this paper. This is an important issue beacuse of its relation to the currently interesting studies in skyrmions in quantum Hall systems. We perform the Hamiltonian analysis of this system in $CP^1$ variables. When the coefficient of the Hopf term becomes zero we get the Landau-Lifshitz description of the ferromagnets. The addition of Hopf term dramatically alters the Hamiltonian analysis. The spin algebra is modified giving a new structure and interpretation to the system. We point out momentum and angular momentum generators and new features they bring in to the system.Comment: 16pages, Latex file, typos correcte

Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.Comment: 24 pages, 3 figures. Title changed, additional material in the Introduction section, the Application section and in the Discussion section highlighting some recent work on singular potentials, several references added. Conclusions remain unchanged. Version matches the version to appear in PR

Beyond fuzzy spheres

We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces, differing by constants, are described by the Higgs algebra at the fuzzy level. Some of these surfaces have a singularity and we overcome this by quantizing this manifold using coherent states for this nonlinear algebra. This is seen in the measure constructed from these coherent states. We also find the star product for this non-commutative algebra as a first step in constructing field theories on such fuzzy spaces.Comment: 9 pages, 3 Figures, Minor changes in the abstract have been made. The manuscript has been modified for better clarity. A reference has also been adde

Information from quantum blackhole physics

The study of BTZ blackhole physics and the cosmological horizon of 3D de Sitter spaces are carried out in unified way using the connections to the Chern Simons theory on three manifolds with boundary. The relations to CFT on the boundary is exploited to construct exact partition functions and obtain logarithmic corrections to Bekenstein formula in the asymptotic regime. Comments are made on the dS/CFT correspondence frising from these studies.Comment: 11 pages; 1 figure(eps file);Talk presented at the conference Space-time and Fundamental Interactions: Quantum Aspects'' in honour of A.P. Balachandran's 65th birthday, Vietri sul Mare, Salerno, Italy 26th-31st May, 200