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Order $1/N^2$ test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary Weyl anomaly

Paul Mansfield·David Nolland·Tatsuya Ueno
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Abstract

We compute the complete bulk one-loop contribution to the Weyl anomaly of the boundary theory for IIB Supergravity compactified on $ AdS_5\times S^5$. The result, that $δ{\cal A}=(E+I)/(2π^2)$, reproduces the subleading term in the exact expression ${\cal A}=-(N^2-1)(E+I)/(2π^2)$ for the Weyl anomaly of ${\cal N}=4$ Super-Yang-Mills theory, confirming the Maldacena conjecture. The anomaly receives contributions from all multiplets casting doubt on the possibility of describing the boundary theory beyond leading order in $N$ by a consistent truncation to the `massless' multiplet of IIB Supergravity.

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Paul Mansfield, David Nolland, Tatsuya Ueno. 2003-05-06. Order $1/N^2$ test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary Weyl anomaly. https://doi.org/10.1016/s0370-2693(03)00750-0

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