Gauge-Invariant Regularisation via SU(N|N)
Abstract
We construct a gauge-invariant regularisation scheme for pure SU(N) Yang-Mills theory in dimension four or less (for N = ∞ in all dimensions), with a physical cutoff scale Λ, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing their powers are within certain ranges, the covariant higher derivatives cure the superficial divergence of all but a set of one-loop graphs. The finiteness of these latter graphs is ensured by properties of the supergroup and gauge invariance. In the limit Λ --> ∞, all the regulator fields decouple and unitarity is recovered in the renormalized pure SU(N) Yang-Mills theory. By demonstrating these properties, we prove that the regularisation works to all orders in perturbation theory.
- Publication:
-
International Journal of Modern Physics A
- Pub Date:
- 2002
- DOI:
- 10.1142/S0217751X02009722
- arXiv:
- arXiv:hep-th/0106258
- Bibcode:
- 2002IJMPA..17.2283A
- Keywords:
-
- Gauge-invariant;
- regularisation;
- exact renormalisation group;
- Yang-Mills;
- non-Abelian gauge theory;
- covariant higher derivatives;
- covariant Pauli-Villars fields;
- High Energy Physics - Theory;
- Condensed Matter;
- High Energy Physics - Lattice;
- High Energy Physics - Phenomenology
- E-Print:
- Latex, 43 pages, extended to explain ERG context, preregularisation and why it is unecessary in less than 4 dimensions or at infinite N, and explain issues in early attempts at gauge invariant Pauli Villars regularisation