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Gauge and Topological Symmetries in the Bulk Quantization of Gauge Theories

L. Baulieu·P. A. Grassi·D. Zwanziger
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Abstract

A gauge theory with 4 physical dimensions can be consistently expressed as a renormalizable topological quantum field theory in 5 dimensions. We extend the symmetries in the 5-dimensional framework to include not only a topological BRST operator S that encodes the invisibility of the "bulk" (the fifth dimension), but also a gauge BRST operator W that encodes gauge-invariance and selects observables. These symmetries provide a rich structure of Ward identities which assure the renormalizability of the theory, including non-renormalization theorems. The 5-dimensional approach considerably simplifies conceptual questions such as for instance the Gribov phenomenon and fermion doubling. A confinement scenario in the 5-dimensional framework is sketched. We detail the five-dimensional mechanism of anomalies, and we exhibit a natural lattice discretization that is free of fermion doubling.

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L. Baulieu, P. A. Grassi, D. Zwanziger. 2000-11-16. Gauge and Topological Symmetries in the Bulk Quantization of Gauge Theories. https://doi.org/10.1016/s0550-3213(00)00725-2

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