A superspace formulation of Yang–Mills theory on sphere

Abstract

A superspace approach to the Becchi–Rouet–Stora–Tyutin (BRST) formalism for the Yang–Mills theory on an n-dimensional unit sphere S1n is developed in a manifestly covariant manner based on the rotational supersymmetry characterized by the supergroup OSp(n+1∣2). This is done by employing an (n+2)-dimensional unit supersphere S1n∣2 parametrized by n commutative and two anticommutative coordinate variables so that it includes S1n as a subspace and realizes the OSp(n+1∣2) supersymmetry. In this superspace formulation, referred to as the supersphere formulation, the so-called horizontality condition is concisely expressed in terms of the rank-3 field strength tensor of a Yang–Mills superfield on S1n∣2. The supersphere formulation completely covers the BRST gauge-fixing procedure for the Yang–Mills theory on S1n provided by us [R. Banerjee and S. Deguchi, Phys. Lett. B 632, 579 (2006); arXiv:hep-th/0509161]. Furthermore, this formulation admits the (massive) Curci–Ferrari model defined on S1n, describing the gauge-fixing and mass terms on S1n together as a mass term on S1n∣2.