N=4 Superconformal Characters and Partition Functions

F.A. Dolan; H. Osborn; M. Bianchi; P.J. Heslop

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N=4 Superconformal Characters and Partition Functions

M. Bianchi, F.A. Dolan, P.J. Heslop, H. Osborn

High Energy Physics - Theory · Submitted 26 Sep 2006

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The authors' main claim 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.

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arXiv IDhep-th/0609179 (version 1)

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CitationF.A. Dolan, H. Osborn, M. Bianchi, P.J. Heslop. "N=4 Superconformal Characters and Partition Functions." arXiv:hep-th/0609179 (2006). https://pith.science/paper/GG7JPFIW

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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 half and some quarter 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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.55	0.89	0.29	asserted 1.00
s1	Expansions of these are given which determine the particular representations present and results such as dimensions of superconformal multiplets.	result 0.67	0.89	0.12	asserted 1.00
s2	By restriction of variables various `blind' characters are also obtained.	result 0.54	0.90	0.04	asserted 1.00
s3	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.	result 0.42	0.86	0.09	asserted 0.92
s4	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.	result 0.94	0.76	0.15	asserted 1.00
s5	Partition functions of N=4 super Yang Mills are investigated.	contribution 0.98	0.83	0.05	asserted 0.87
s6	Through analysis of these, exact formulae are obtained for counting half and some quarter BPS operators in the free case.	result 0.98	0.93	0.16	asserted 1.00
s7	Similarly, partial results for the counting of semi-short operators are given.	result 0.83	0.90	0.06	asserted 0.97
s8	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.	result 0.94	0.87	0.11	asserted 0.83

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Original 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 half and some quarter 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.

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23 arXiv papers cite this in 46 sentences

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By taking the various decoupling limits we obtain expressions for $⟨D_2(x̃)⟩$ in each decoupled theory.[One can also compute $⟨D_2⟩$ in the decoupled theories using the general procedure found in [ref] .]

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When there are bulk fermionic degrees of freedom to be summed over, as in the case of supersymmetric theories, it is sufficient to use the CIRZ method as presented for bosons, but instead of using the thermal partition function, use the weighted partition function [equation] introduced in [ref] .

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Following [ref] , we start with the Verma module character of the highest-weight state in the superconformal multiplet and we generate the Verma module character for the associated $𝔬𝔰𝔭(4^*|4)$ representation multiplying with characters associated to translations and to the supercharges that do not annihilate the superconformal primary.

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