Abstract: |
In this talk I will present some ongoing work on indices of 4d N=2 SCFTs. By coupling a flat-space supersymmetric theory to a rigid supergravity background, we may define its curved space analogue, while preserving some supersymmetry. The partition function of such a theory placed on S3xS1 determines an index with fugacities related to the various background supergravity fields. In the first part of the talk, I will briefly review how this construction works for 4d N=2 SCFTs. With a suitable choice of supergravity background fields, I will show how to recover the superconformal index and the twisted index. In the second part of the talk, I will construct a so-called "interpolating" supergravity background which takes us from the superconformal to the twisted configuration, while preserving some supersymmetry. I will further show that this interpolation is in fact exact and the resulting partition function is independent of the interpolating parameter. This allows us to identify the superconformal index with the twisted one. I will conclude by commenting on that identification of the indices. |