Supersymmetric indices, defects and holography

Abstract

This thesis explores the use of holography in the study of codimension-2 and codimension-4 defects of the 6d N = (2, 0) theories. By means of the Ryu-Takayanagi formula, we successfully determine various central charges associated to these defects, which play a crucial role in their full characterization. We also establish connections between different families of supergravity solutions, delivering a more comprehensive picture of their landscape.

Another focus of this thesis is that of background conformal supergravity configurations for 4d N = 2 and 4d N = 4 SCFTs. The departure from the holographic tools is nevertheless an interesting one, as we are able to find such backgrounds that engineer various topological twists of the theories. Our results are novel in the context of N = 4,where we are able to construct the supercharges of the Vafa-Witten, Kapustin-Witten and half-twists, all valuable non-perturbative tools in the study of four-dimensional theories. Backgrounds for the N = 2 indices were already known, however, we provide a novel family of indices that interpolates exactly between the twisted index and a point on the moduli of Coulomb-branch indices; allowing us to equate the two.

Finally, we introduce a novel realisation of defect-conformal-field-theories as finite-dimensional integrals over neural-networks. This construction extends the known formalism for CFTs to the defect case, providing a systematic framework for generating dCFT data from neural-network concatenations.

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Identifiers

ORCID for Benjamin Suzzoni: orcid.org/0000-0002-3941-0256

ORCID for Itamar Yaakov: orcid.org/0000-0002-4924-2970

ORCID for Andrew H O'Bannon: orcid.org/0000-0001-7862-783X

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