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,...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
2015
|
| In: |
Arxiv
|
| Online Access: | Verlag, kostenfrei, Volltext: http://arxiv.org/abs/1506.08407
|
| Author Notes: | Marc-Antoine Fiset, Johannes Walcher |
| Summary: | 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. |
|---|---|
| Item Description: | Gesehen am 25.02.2020 |
| Physical Description: | Online Resource |