arXiv subjects
Publications and source records attributed to Stefano Chiantese.
We compute the anomalies of the topological A and B models with target space geometry of Hitchin's generalized type. The dimension of the moduli space of generalized holomorphic maps is also computed, which turns out to be equal to the total anomaly if the moduli space is unobstructed. We obtain this result by identifying the infinitesimal deformations of such maps and by using the Grothendieck-Riemann-Roch formula.
The existence of a new kind of branes for the open topological A-model is argued by using the generalized complex geometry of Hitchin and the SYZ picture of mirror symmetry. Mirror symmetry suggests to consider a bi-vector in the normal direction of the brane and a new definition of generalized complex submanifold. Using this definition, it is shown that there exists generalized complex submanifolds which are isotropic in a symplectic manifold. For certain target space manifolds this leads to isotropic A-branes, which should be considered in addition to Lagrangian and coisotropic A-branes. The Fukaya category should be enlarged with such branes, which might have interesting consequences for the homological mirror symmetry of Kontsevich. The stability condition for isotropic A-branes is studied using the worldsheet approach.
We consider topological sigma models with generalized Kahler target spaces. The mirror map is constructed explicitly for a special class of target spaces and the topological A and B model are shown to be mirror pairs in the sense that the observables, the instantons and the anomalies are mapped to each other. We also apply the construction to open topological models and show that A branes are mapped to B branes. Furthermore, we demonstrate a relation between the field strength on the brane and a two-vector on the mirror manifold.
We use free boson techniques to investigate A-D-E-quiver matrix models. Certain higher spin fields in the free boson formulation give rise to higher order loop equations valid at finite N. These fields form a special kind of W-algebra, called Casimir algebra. We compute explicitly the loop equations for A_r and D_r quiver models and check that at large N they are related to a deformation of the corresponding singular Calabi-Yau geometry.