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TUE: Tuesday Contributed Sessions
TUE 3: Quantum Field Theory
TUE 3.4: Vortrag
Dienstag, 9. September 2025, 15:00–15:15, ZHG003
Spinorial Superspaces and Supersymmetric Yang-Mills Theories — •Johannes Moerland — University of Göttingen
In physics literature about supersymmetry, many authors refer to "super Minkowski spaces". These spaces are extensions of ordinary Minkowski spaces by spinorial directions. More abstractly, super Minkowski spaces are affine supermanifolds (i.e., locally ringed spaces with a Z2-graded algebra of functions) with distinguished spin structures.
In this talk, we formalise these spin structures, allowing us to generalise the setup to curved supermanifolds. Apart from the possibility of formulating field theories on topologically non-trivial superspaces, our approach bears two advantages: Firstly, the language of graded geometry allows for a global and inherently coordinate-free formulation of field theories on the superspace. Secondly, the approach to superspaces via graded geometry endows many algebraic manipulations with a concise geometric meaning. For example, the Dirac γ matrices can be identified with the torsion of the superspace along the spinorial directions.
After exploring the geometric properties of spinorial superspaces, we apply the rather general theory to N=1 super Yang-Mills theories on curved superspaces of space-time dimensions 3 and 4 and show that the effective theory on an embedded ordinary space-time manifold, obtained by integrating over the spinorial directions, reproduces a coupled system of Yang-Mills and twisted Dirac Lagrangians.
Keywords: Supersymmetry; Graded Geometry; Field Theory; Gauge Theory