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arXiv · 2206.14522

On type IIB supergravity action on $M^5 \times X^5$ solutions

S. A. Kurlyand·A. A. Tseytlin
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Abstract

While the 10d type IIB supergravity action evaluated on AdS$_5\times S^5$ solution vanishes, the 5d effective action reconstructed from the equations of motion using $M^5 \times S^5$ compactification ansatz is proportional to the AdS$_5$ volume. The latter is consistent with the conformal anomaly interpretation in AdS/CFT context. We show that this paradox can be resolved if, in the case of $M^5 \times X^5$ topology, the 10d action contains an additional 5-form dependent "topological" term $\int F_{5M} \wedge F_{5X}$. The presence of this term is suggested also by gauge-invariance considerations in the PST formulation of type IIB supergravity action. We show that this term contributes to the 10d action evaluated on the D3-brane solution.

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S. A. Kurlyand, A. A. Tseytlin. 2022-10-06. On type IIB supergravity action on $M^5 \times X^5$ solutions. https://doi.org/10.1103/physrevd.106.086017

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