Supergravity one-loop corrections on AdS7 and AdS3, higher spins and AdS/CFT

As was shown earlier, the one-loop correction in 10d supergravity on AdS(5) x S-5 corresponds to the contributions to the vacuum energy and 4d boundary conformal anomaly which are minus the values for one N = 4 Maxwell supermultiplet, thus reproducing the subleading term in the N-2 - 1 coefficient in the dual SU(N) SYM theory. We perform similar one-loop computations in lid supergravity on AdS(7) x S-4 and 10d supergravity on AdS(3) x S-3 x T-4. In the AdS(7) case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2, 0) tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2,0) theory is 4N(3) - 9/4N - 7/4 and thus vanishes for N = 1. In the AdS(3) case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4, 4) scalar multiplet, i.e. is c = +6. This reproduces the subleading term in the central charge c = 6(Q(1)Q(5) + 1) of the dual 2d CFT describing decoupling limit of D5-D1 system. We also 'present the expressions for the 6d a-anomaly coefficient and vacuum energy contributions of general-symmetry higher spin field in AdS(7) and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank-2 antisymmetric tensors. (C) 2015 The Authors. Published by Elsevier B.V.