2009/05/31 by Rabin Banerjee, Shinichi Deguchi
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.3377047
published as J. Math. Phys. 51:052301,2010 · 36 pages, no figure, minor corrections
arxiv created 2010/06/12 · arxiv updated 2014/11/18
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 2 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 (2006) 579, 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.