Curved A-infinity algebras and Landau-Ginzburg models

Mathematics – K-Theory and Homology

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

42pp, LaTeX

Scientific paper

We study the Hochschild homology and cohomology of curved A-infinity algebras that arise in the study of Landau-Ginzburg (LG) models in physics. We show that the ordinary Hochschild homology and cohomology of these algebras vanish. To correct this we introduce modified versions of these theories, Borel-Moore Hochschild homology and compactly supported Hochschild cohomology. For LG models the new invariants yield the answer predicted by physics, shifts of the Jacobian ring. We also study the relationship between graded LG models and the geometry of hypersurfaces. We prove that Orlov's derived equivalence descends from an equivalence at the differential graded level, so in particular the CY/LG correspondence is a dg equivalence. This leads us to study the equivariant Hochschild homology of orbifold LG models. The results we get can be seen as noncommutative analogues of the Lefschetz hyperplane and Griffiths transversality theorems.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Curved A-infinity algebras and Landau-Ginzburg models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Curved A-infinity algebras and Landau-Ginzburg models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curved A-infinity algebras and Landau-Ginzburg models will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-50415

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.