Abstract
We show, by introducing purely auxiliary gluinos and scalars, that the quantum path integral for a class of 3D interacting non-supersymmetric gauge theories localises. The theories in this class all admit a ‘Manin gauge theory’ formulation, that we introduce; it is obtained by enhancing the gauge algebra of the theory to a Dirac structure inside a Manin pair. This machinery allows us to do localisation computations for every theory in this class at once, including for 3D Yang-Mills theory, and for its Third Way deformation; the latter calculation casts the Third Way path integral into an almost 1-loop exact form.
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Details
1 Vrije Universiteit Brussel, and the International Solvay Institutes, Theoretische Natuurkunde, Brussels, Belgium (GRID:grid.8767.e) (ISNI:0000 0001 2290 8069); Division of Theoretical Physics, Ruđer Bošković Institute, Zagreb, Croatia (GRID:grid.4905.8) (ISNI:0000 0004 0635 7705)
2 Vrije Universiteit Brussel, and the International Solvay Institutes, Theoretische Natuurkunde, Brussels, Belgium (GRID:grid.8767.e) (ISNI:0000 0001 2290 8069); University of Hertfordshire, Department of Physics, Astronomy and Mathematics, Hatfield, U.K. (GRID:grid.5846.f) (ISNI:0000 0001 2161 9644)