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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.

##### MSC:
 81T50 Anomalies in quantum field theory 81T60 Supersymmetric field theories in quantum mechanics 83E30 String and superstring theories in gravitational theory
##### Keywords:
conformal anomaly
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