STRUCTURES Team

Fields of Interest:
Supersymmetric Field Theory, Pure Spinor Formalism, BV/BRST Formalism, Twisted Supersymmetric Field Theory and Supergravity

Short summary of current research:
I'm interested in the systematic construction of supersymmetric field theories. Here my method of choice is the pure spinor superfield formalism (https://arxiv.org/abs/2111.01162) which systematizes earlier approaches from the physics literature using homological algebra and algebraic geometry. We used a 'derived' enhancement of the formalism to prove that there is an equivalence of categories between supermultiplets and a certain category of modules (https://arxiv.org/abs/2205.14133). These results can be applied in various directions: for example we classify a certain class of multiplets using simple well known things from geometry such as line bundles on projective spaces (https://arxiv.org/abs/2206.08388). Supersymmetric field theories are interesting for mathematics because they can be twisted! Observables in the twisted theory measure a smooth or holomorphic structure of the spacetime manifold (that's amazing, isn't it?). I really would like to understand twisted supergravity theories, what they measure and their holographic dual. As the first step in this endeavour, we computed the maximal twist of eleven-dimensional supergravity (https://arxiv.org/abs/2106.15640).

Contact:
fhahner[]mathi.uni-heidelberg.de