109 research outputs found
On the unipotence of autoequivalences of toric complete intersection Calabi-Yau categories
We identify a class of autoequivalences of triangulated categories of
singularities associated with Calabi-Yau complete intersections in toric
varieties. Elements of this class satisfy relations that are directly linked to
the toric data.Comment: 17 page
Matrix Factorizations and Kauffman Homology
The topological string interpretation of homological knot invariants has led
to several insights into the structure of the theory in the case of sl(N). We
study possible extensions of the matrix factorization approach to knot homology
for other Lie groups and representations. In particular, we introduce a new
triply graded theory categorifying the Kauffman polynomial, test it, and
predict the Kauffman homology for several simple knots.Comment: 45 pages, harvma
Bounding the Heat Trace of a Calabi-Yau Manifold
The SCHOK bound states that the number of marginal deformations of certain
two-dimensional conformal field theories is bounded linearly from above by the
number of relevant operators. In conformal field theories defined via sigma
models into Calabi-Yau manifolds, relevant operators can be estimated, in the
point-particle approximation, by the low-lying spectrum of the scalar Laplacian
on the manifold. In the strict large volume limit, the standard asymptotic
expansion of Weyl and Minakshisundaram-Pleijel diverges with the higher-order
curvature invariants. We propose that it would be sufficient to find an a
priori uniform bound on the trace of the heat kernel for large but finite
volume. As a first step in this direction, we then study the heat trace
asymptotics, as well as the actual spectrum of the scalar Laplacian, in the
vicinity of a conifold singularity. The eigenfunctions can be written in terms
of confluent Heun functions, the analysis of which gives evidence that regions
of large curvature will not prevent the existence of a bound of this type. This
is also in line with general mathematical expectations about spectral
continuity for manifolds with conical singularities. A sharper version of our
results could, in combination with the SCHOK bound, provide a basis for a
global restriction on the dimension of the moduli space of Calabi-Yau
manifolds.Comment: 32 pages, 3 figure
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