6 research outputs found
On the full, strongly exceptional collections on toric varieties with Picard number three
We investigate full strongly exceptional collections on smooth, com- plete
toric varieties. We obtain explicit results for a large family of varieties
with Picard number three, containing many of the families already known. We
also describe the relations between the collections and the split of the push
forward of the trivial line bundle by the toric Frobenius morphism
On Pure Spinor Superfield Formalism
We show that a certain superfield formalism can be used to find an off-shell
supersymmetric description for some supersymmetric field theories where
conventional superfield formalism does not work. This "new" formalism contains
even auxiliary variables in addition to conventional odd super-coordinates. The
idea of this construction is similar to the pure spinor formalism developed by
N.Berkovits. It is demonstrated that using this formalism it is possible to
prove that the certain Chern-Simons-like (Witten's OSFT-like) theory can be
considered as an off-shell version for some on-shell supersymmetric field
theories. We use the simplest non-trivial model found in [2] to illustrate the
power of this pure spinor superfield formalism. Then we redo all the
calculations for the case of 10-dimensional Super-Yang-Mills theory. The
construction of off-shell description for this theory is more subtle in
comparison with the model of [2] and requires additional Z_2 projection. We
discover experimentally (through a direct explicit calculation) a non-trivial
Z_2 duality at the level of Feynman diagrams. The nature of this duality
requires a better investigation
Seiberg Duality is an Exceptional Mutation
The low energy gauge theory living on D-branes probing a del Pezzo
singularity of a non-compact Calabi-Yau manifold is not unique. In fact there
is a large equivalence class of such gauge theories related by Seiberg duality.
As a step toward characterizing this class, we show that Seiberg duality can be
defined consistently as an admissible mutation of a strongly exceptional
collection of coherent sheaves.Comment: 32 pages, 4 figures; v2 refs added, "orbifold point" discussion
refined; v3 version to appear in JHEP, discussion of torsion sheaves improve
Mutation in triangulated categories and rigid Cohen-Macaulay modules
We introduce the notion of mutation of -cluster tilting subcategories in a
triangulated category with Auslander-Reiten-Serre duality. Using this idea, we
are able to obtain the complete classifications of rigid Cohen-Macaulay modules
over certain Veronese subrings.Comment: 52 pages. To appear in Invent. Mat