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Conformal anomaly of \((2,0)\) tensor multiplet in six dimensions and AdS/CFT correspondence. (English) Zbl 0959.81088
Summary: We compute the conformal anomaly in the free \(d=6\) superconformal \((2,0)\) tensor multiplet theory on generic curved background. Up to a trivial covariant total-derivative term, it is given by the sum of the type A part proportional to the 6-d Euler density, and the type B part containing three independent conformal invariants: two CCC contractions of Weyl tensors and a \(C\nabla^2C +\dots\) term. Multiplied by the factor \(4N^3\), the latter Weyl-invariant part of the anomaly reproduces exactly the corresponding part of the conformal anomaly of large \(N\) multiple M5-brane \((2,0)\) theory as predicted [M. Henningson and K. Skenderis, The holographic Weyl anomalies, ibid. 1998, Paper No. 07(1998)023 (1998; Zbl 0958.81083)] by \(\text{AdS}_7\) supergravity on the basis of AdS/CFT correspondence. The coefficients of the type A anomaly differ by the factor \(4/7 \times 4 N^3\), so that the free tensor multiplet anomaly does not vanish on a Ricci-flat background. The coefficient \(4N^3\) is the same as found [S. S. Gubser, I. R. Klebanov and A. A. Tseytlin, Nucl. Phys. B 499, 217-240 (1997; Zbl 0959.81046)] in the comparison of the tensor multiplet theory and the \(d=11\) supergravity predictions for the absorption cross-sections of gravitons by M5 branes, and in the comparison [the authors, Nucl. Phys. B 578, 139-152 (2000)] of 2- and 3-point stress tensor correlators of the free tensor multiplet with the \(\text{AdS}_7\) supergravity predictions. The reason for this coincidence is that the three Weyl-invariant terms in the anomaly are related to the \(h^2\) and \(h^3\) terms in the near flat-space expansion of the corresponding non-local effectiveaction, and thus to the 2-point and 3-point stress tensor correlators in flat background. At the same time, the type A anomaly is related to the \(h^4\) term in the non-local part of the effective action, i.e. to a certain structure in the 4-point correlation function of the stress tensors. It should thus capture some non-trivial dynamics of the interacting theory. This is different from what happens in the \(d=4\) SYM case where the type B and type A anomalies are related to the 2-point and 3-point stress tensor correlators.

81T50 Anomalies in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
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