Sp(2) Renormalization

TL;DR

This paper demonstrates that Sp(2)-covariant quantization ensures gauge and diffeomorphism invariant renormalization of general gauge theories on flat and curved backgrounds, simplifying the treatment of ghosts and auxiliary fields.

Contribution

It shows that the Sp(2)-covariant formalism guarantees all-order renormalizability and preserves extended BRST symmetry, offering a systematic approach for reducible theories.

Findings

Gauge and diffeomorphism invariant renormalization is achieved to all orders.

Sp(2) formalism simplifies the structure of ghosts and auxiliary fields.

Extended BRST symmetry remains preserved after renormalization.

Abstract

The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST symmetry after renormalization is preserved. The advantage of the Sp(2)-method compared to the standard Batalin-Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)- scalars.