The Boundary Weyl Anomaly in the $\mathcal{N}=4$ SYM/Type IIB Supergravity Correspondence

Abstract

We give a complete account of the Schrödinger representation approach to the calculation of the Weyl anomaly of $\mathcal{N}=4$ SYM from the AdS/CFT correspondence. On the AdS side, the $1/N^2$ correction to the leading order result receives contributions from all the fields of Type IIB Supergravity, the contribution of each field being given by a universal formula. The correct matching with the CFT result is thus a highly non-trivial test of the correspondence.

arXiv comment30 pages

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• 1/N^2 corrections to the holographic Weyl anomaly
• Central charges from the $\mathcal{N}=1$ superconformal index
• The spectrum of IIB supergravity on AdS_5 x S^5/Z_3 and a 1/N^2 test of AdS/CFT
• Exact strong coupling results in $\mathcal{N}$=2 $Sp(2N)$ superconformal gauge theory from localization
• Divergences and Boundary Modes in N=8 Supergravity
• The shortened KK spectrum of IIB supergravity on Y^{p,q}
• Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all
• One-Loop Free Energy of Tensionless Type IIB String in AdS${}_5\times$S${}^5$
• One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory
• The Weyl Anomaly from the 6D Superconformal Index
• Holographic spectral functions for Sasaki-Einstein 5-manifolds
• Boundary fermion currents and subleading order chiral anomaly in the AdS/CFT correspondence
• AdS/CFT boundary conditions and multi-trace perturbations for fermions