Correspondence between the twisted $N=2$ super-Yang-Mills and conformal Baulieu-Singer theories

Abstract

We characterize the correspondence between the twisted $N=2$ super-Yang-Mills theory and the Baulieu-Singer topological theory quantized in the self-dual Landau gauges. While the first is based on an on-shell supersymmetry, the second is based on an off-shell Becchi-Rouet-Stora-Tyutin symmetry. Because of the equivariant cohomology, the twisted $N=2$ in the ultraviolet regime and Baulieu-Singer theories share the same observables, the Donaldson invariants for 4-manifolds. The triviality of the Gribov copies in the Baulieu-Singer theory in these gauges shows that working in the instanton moduli space on the twisted $N=2$ side is equivalent to working in the self-dual gauges on the Baulieu-Singer one. After proving the vanishing of the $\beta$ function in the Baulieu-Singer theory, we conclude that the twisted $N=2$ in the ultraviolet regime, in any Riemannian manifold, is correspondent to the Baulieu-Singer theory in the self-dual Landau gauges -- a conformal gauge theory defined in Euclidean flat space.

41 pages. Accepted for publication in PRD. Updated version

References in corpus (12)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that
• Soft breaking of BRST invariance for introducing non-perturbative infrared effects in a local and renormalizable way
• Gribov horizon and BRST symmetry: a few remarks
• Introduction to the Gribov Ambiguities In Euclidean Yang-Mills Theories
• An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions
• On the irrelevance of the Gribov issue in N=4 Super Yang-Mills in the Landau gauge
• Topological Gravity as the Early Phase of Our Universe
• A study of the Gribov-Zwanziger action: from propagators to glueballs
• Topological Yang-Mills theories in self-dual and anti-self-dual Landau gauges revisited
• From propagators to glueballs in the Gribov-Zwanziger framework

Cited by in corpus (2)

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