Character formulae for positive energy unitary representations of the N = 4 superconformal group are obtained through use of reduced Verma modules and Weyl group symmetry. Expansions of these are given which determine the particular representations present and results such as dimensions of superconformal multiplets. By restriction of variables various 'blind' characters are also obtained. Limits, corresponding to reduction to particular subgroups, in the characters isolate contributions from particular subsets of multiplets and in many cases simplify the results considerably. As a special case, the index counting short and semi-short multiplets which do not form long multiplets found recently is shown to be related to particular cases of reduced characters. Partition functions of N = 4 super-Yang-Mills are investigated. Through analysis of these, exact formulae are obtained for counting 1/2- and some 1/4-BPS operators in the free case. Similarly, partial results for the counting of semi-short operators are given. It is also shown in particular examples how certain short operators which one might combine to form long multiplets due to group theoretic considerations may be protected dynamically.

Bianchi, M., Dolan, F.a., Heslop, P.j., Osborn, H. (2007). N = 4 superconformal characters and partition functions. NUCLEAR PHYSICS. B, 767(3), 163-226 [10.1016/j.nuclphysb.2006.12.005].

N = 4 superconformal characters and partition functions

Bianchi M.;
2007-01-01

Abstract

Character formulae for positive energy unitary representations of the N = 4 superconformal group are obtained through use of reduced Verma modules and Weyl group symmetry. Expansions of these are given which determine the particular representations present and results such as dimensions of superconformal multiplets. By restriction of variables various 'blind' characters are also obtained. Limits, corresponding to reduction to particular subgroups, in the characters isolate contributions from particular subsets of multiplets and in many cases simplify the results considerably. As a special case, the index counting short and semi-short multiplets which do not form long multiplets found recently is shown to be related to particular cases of reduced characters. Partition functions of N = 4 super-Yang-Mills are investigated. Through analysis of these, exact formulae are obtained for counting 1/2- and some 1/4-BPS operators in the free case. Similarly, partial results for the counting of semi-short operators are given. It is also shown in particular examples how certain short operators which one might combine to form long multiplets due to group theoretic considerations may be protected dynamically.
2007
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore FIS/02 - FISICA TEORICA, MODELLI E METODI MATEMATICI
English
superconformal symmetry
N=4 quantum field theory
characters
partition functions
Bianchi, M., Dolan, F.a., Heslop, P.j., Osborn, H. (2007). N = 4 superconformal characters and partition functions. NUCLEAR PHYSICS. B, 767(3), 163-226 [10.1016/j.nuclphysb.2006.12.005].
Bianchi, M; Dolan, Fa; Heslop, Pj; Osborn, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/289603
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