Symmetries, Protected Quantities, and Exact Computations in Supergravity

Symmetries, Protected Quantities, and Exact Computations in Supergravity

Recent years have witnessed a surge of exact computations of supersymmetry-protected observables in supergravity. These results anchor some of the sharpest quantitative tests of the AdS/CFT correspondence to date. While examples are increasingly plentiful, their deeper formal underpinnings remain elusive. Several diverse perspectives and approaches shed partial light, but their relations to one another remain unclear. The core structures must lie at the intersection of these various mutually illuminating strands.

The universal superfield formulations of supersymmetry supplied by the pure spinor superfield formalism have quietly lifted a longstanding technical obstacle to performing calculations in the spirit of supersymmetric localization. In doing so, they recast supergravity as a theory of deformations of a non-holonomic distribution in derived geometry, with gauge symmetries governed by infinite-dimensional Lie superalgebras that arise as tangent complexes to their moduli. This approach offers a new ringed-space perspective on issues that are traditionally treated using ideas from Cartan geometry to build superspace techniques. In parallel, the twisted supergravity program reframes the same protected quantities inside holomorphic-topological sectors, offering a complementary perspective that streamlines localization-based computations while clarifying their geometric provenance. Dualities can be made rigorous within twisted supergravity, but appear most naturally within approaches using generalized or exceptional geometry, which have undergone rapid development recently, uncovering striking structural similarities to BCOV theory while tying supergravity to the deformation theory of exceptional or generalized geometric structures. Taken together, these viewpoints outline a coherent narrative that bridges geometry, homotopical algebra, and supergravity.

A central goal of the workshop is to create a common language among these diverse approaches and the communities that work on them, encouraging participants to share perspectives and identify deep structural similarities. By bringing together complementary viewpoints, the workshop aims to initiate collaborations across areas that are often pursued in parallel but rarely in conversation. In addition to overviews and perspectives by experts in each approach, the format will include focused talks, ample discussion time, and opportunities for informal interaction.