Superspace calculation of the four-loop spectrum in \(\mathcal{N} = 6\) supersymmetric Chern-Simons theories. (English) Zbl 1294.81118
Summary: Using \(\mathcal{N} = 2\) superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) {\(\times\)} SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function \(h^{2}(\lambda)\) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of [The \(3^{rd}\), \(4^{th}\) and \(6^{th}\)author, J. Phys. A, Math. Theor. 43, No. 27, Article ID 275402, 17 p. (2010); corrigendum 44, No. 4, Article ID, 2 p. (2011; Zbl 1193.81089)] and [The \(3^{rd}\), \(4^{th}\) and \(6^{th}\)author, Nucl. Phys., B 846, No. 3, 542-606 (2011; Zbl 1208.82011)]. We also discuss possible scenarios for an all-loop function \(h^{2}(\lambda)\) that interpolates between weak and strong couplings.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 58J28 | Eta-invariants, Chern-Simons invariants |
| 46S60 | Functional analysis on superspaces (supermanifolds) or graded spaces |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
Keywords:
supersymmetric gauge theory; superspaces; AdS-CFT correspondence; integrable field theoriesReferences:
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