1994/07/22 by José Figueroa-O’Farrill, J M Figueroa-O'Farrill, Figueroa-O'Farrill, J M +3 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9407149
uuencoded compressed .ps file, 45 pages, QMW-PH-94-17. (a few more typographical errors, notational inconsistencies, and the embarrassing Cor. 7.6 corrected. our sincere apologies for the wasted bandwidth and/or paper.)
openalex publication_date 1994/07/22 · arxiv created 1994/07/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We re-examine the problem of gauging the Wess-Zumino term of a d-dimensional bosonic sigma-model. We phrase this problem in terms of the equivariant cohomology of the target space and this allows for the homological analysis of the obstruction. As a check, we recover the obstructions of Hull and Spence and also a generalization of the topological terms found by Hull, Rocek and de Wit. When the symmetry group is compact, we use topological tools to derive vanishing theorems which guarantee the absence of obstructions for low dimension (d<=4) but for a variety of target manifolds. For example, any compact semisimple Lie group can be gauged in a three-dimensional sigma-model with simply connected target space. When the symmetry group is semisimple but not necessarily compact, we argue in favor of the persistence of these vanishing theorems by making use of (conjectural) equivariant minimal models (in the sense of Sullivan). By way of persuasion, we construct by hand a few such equivariant minimal models, which may be of independent interest. We illustrate our results with two examples: d=1 with a symplectic target space, and d=2 with target space a Lie group admitting a bi-invariant metric. An alternative homological interpretation of the obstruction is obtained by a closer study of the Noether method. This method displays the obstruction as a class in BRST cohomology at ghost number 1. We comment on the relationship with consistent anomalies.