ON THE CHIRAL RINGS IN N=2 AND N=4 SUPERCONFORMAL ALGEBRAS
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Publication:4301118
DOI10.1142/S0217751X93000126zbMATH Open0801.17035arXivhep-th/9207023MaRDI QIDQ4301118
Publication date: 5 December 1994
Published in: International Journal of Modern Physics A (Search for Journal in Brave)
Abstract: We study the chiral rings in N=2 and N=4 superconformal algebras. The chiral primary states of N=2 superconformal algebras realized over hermitian triple systems are given. Their coset spaces G/H are hermitian symmetric which can be compact or non-compact. In the non-compact case, under the requirement of unitarity of the representations of G we find an infinite set of chiral primary states associated with the holomorphic discrete series representations of G. Further requirement of the unitarity of the corresponding N=2 module truncates this infinite set to a finite subset. The chiral primary states of the N=2 superconformal algebras realized over Freudenthal triple systems are also studied. These algebras have the special property that they admit an extension to N=4 superconformal algebras with the gauge group SU(2)XSU(2)XU(1). We generalize the concept of the chiral rings to N=4 superconformal algebras. We find four different rings associated with each sector (left or right moving). We also show that our analysis yields all the possible rings of N=4 superconformal algebras.
Full work available at URL: https://arxiv.org/abs/hep-th/9207023
Applications of Lie (super)algebras to physics, etc. (17B81) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Ternary compositions (17A40)
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