One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory

Abstract

The large-$N$ limit of ABJM theory is holographically dual to M-theory on AdS${}_4\times S^7/{\mathbb{Z}}_k$. The 3-sphere partition function has been obtained via localization, and its leading behavior $F_{\text{ABJM}}^{(0)}\sim k^{1/2}{N}^{3/2}$ is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading $\mathcal{O}(N^0)$ order by computing the one-loop supergravity free energy as a function of $k$ and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with $F_{\text{SUGRA}}^{(1)}\sim k^6$, while $F_{\text{ABJM}}^{(1)}\sim k^2$. This suggests that the low-energy approximation $Z_{\text{M-theory}}=Z_{\text{SUGRA}}$ breaks down at one-loop order.

arXiv comment22 pages, 1 figure, discussion on the O(N^{1/2}) order and references added

References in corpus (23)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Holographic Weyl anomaly
• Holographic c-theorems in arbitrary dimensions
• From weak to strong coupling in ABJM theory
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Nonperturbative aspects of ABJM theory
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades
• Anomalous radius shift in AdS(4)/CFT(3)
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• A Note on the Chiral Anomaly in the AdS/CFT Correspondence and 1/N^2 Correction
• On Superconformal Characters and Partition Functions in Three Dimensions
• A Note on the Partition Function of ABJM theory on S^3
• 1/N^2 corrections to the holographic Weyl anomaly
• Order 1/N^2 test of the Maldacena conjecture: Cancellation of the one-loop Weyl anomaly
• $c-a$ from the $N=1$ superconformal index
• Order $1/N^2$ test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary 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
• The Boundary Weyl Anomaly in the $\mathcal{N}=4$ SYM/Type IIB Supergravity Correspondence
• The shortened KK spectrum of IIB supergravity on Y^{p,q}

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• ABJ Quadrality
• Spin Structures and AdS${}_4$ Holography
• The Holographic Contributions to the Sphere Free Energy