Universal Schwinger cocycles of current algebras in \((D+1)\)-dimensions: Geometry and physics (Q753230)

The authors study the universal version of the Schwinger terms of current algebras and call them the universal Schwinger cocycles. If p is the class of the Schatten ideal, this cocycle is explicitly computed for \(p=3\) generalizing the Kac-Peterson result for \(p=1\) and the Michelsson- Rajeev formula for \(p=2\). In addition, a general formula for this cocycle is conjectured and it is shown that the Jacobi identity for it holds. Infinite charge renormalizations and highest weight and state vectors are also presented explicitly for low p, and formulae for \(p\geq 4\) are conjectured.