Chang, Zhihua; Pianzola, Arturo On twisted large \(N=4\) conformal superalgebras. (English) Zbl 1294.81241 Adv. Theor. Math. Phys. 17, No. 6, 1393-1415 (2013). Summary: We explicitly compute the automorphism group of the large \(N=4\) conformal superalgebra and classify the twisted loop conformal superalgebras based on the large \(N=4\) conformal superalgebra. By considering the corresponding superconformal Lie algebras, we validate the existence of only, two (up to isomorphism) such algebras as described in the physics literature. Our approach is based on viewing the objects to be classified as “étale twisted forms” of objects over the Laurent polynomial ring \(\mathbb C[t^{\pm 1}]\). This allows methods from non-abelian cohomology (torsors) to enter into the picture. It is worth pointing out that the group of automorphisms of the large \(N = 4\) conformal superalgebra is larger than the one described in the physics literature. Remarkably enough, both groups have the same étale cohomology over \(\mathbb C[t^{\pm 1}]\) which explains the agreement on the classification of the corresponding superconformal Lie algebras). Cited in 1 Document MSC: 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 17A70 Superalgebras 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) × Cite Format Result Cite Review PDF Full Text: DOI arXiv