Brewing moonshine for Mathieu

We propose a moonshine for the sporadic Mathieu group M_12 that relates its conjugacy classes to various modular forms and Borcherds Kac-Moody Lie superalgebras.Comment: 21 pages; LaTeX; no figure

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

Estimating the asymptotics of solid partitions

We study the asymptotic behavior of solid partitions using transition matrix Monte Carlo simulations. If $p_3(n)$ denotes the number of solid partitions of an integer $n$, we show that $\lim_{n\rightarrow\infty} n^{-3/4} \log p_3(n)\sim 1.822\pm 0.001$. This shows clear deviation from the value $1.7898$, attained by MacMahon numbers $m_3(n)$, that was conjectured to hold for solid partitions as well. In addition, we find estimates for other sub-leading terms in $\log p_3(n)$. In a pattern deviating from the asymptotics of line and plane partitions, we need to add an oscillatory term in addition to the obvious sub-leading terms. The period of the oscillatory term is proportional to $n^{1/4}$, the natural scale in the problem. This new oscillatory term might shed some insight into why partitions in dimensions greater than two do not admit a simple generating function.Comment: 21 pages, 8 figure

Worldsheet approaches to D-branes on supersymmetric cycles

We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau-Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy's procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using the common discrete symmetries of the two descriptions. We are thus able to provide an extension to the boundary of the bulk correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner models.Comment: 28 pages, LaTeX with revtex; (v2) Condition involving superpotential in the boundary LG model imposed, references included ; (v3) final version to appear in journa