Flowing from $Ad{S}_5$ to $Ad{S}_3$ with $T^{1,1}$

Abstract

We construct supersymmetric domain wall solutions of type IIB supergravity that interpolate between $Ad{S}_5\times T^{1,1}$ in the UV and $Ad{S}_3\times {\mathbb{R}}^2\times S^2\times S^3$ solutions in the IR. The ${\mathbb{R}}^2$ factor can be replaced with a two-torus and then the solution describes a supersymmetric flow across dimensions, similar to wrapped brane solutions. While the domain wall solutions preserve $(0,2)$ supersymmetry, the $Ad{S}_3$ solutions in the IR have an enhanced $(4,2)$ superconformal supersymmetry and are related by two T-dualities to the $Ad{S}_3\times S^3\times S^3\times S^1$ type IIB solutions which preserve a large $(4,4)$ superconformal supersymmetry. The domain wall solutions exist within the $N=4$ $D=5$ gauged supergravity theory that is obtained from a consistent Kaluza-Klein truncation of type IIB supergravity on $T^{1,1}$; a feature driving the flows is that two $D=5$ axion like fields, residing in the $N=4$ Betti multiplet, depend linearly on the two legs of the ${\mathbb{R}}^2$ factor.

arXiv comment35 pages, 1 figure. References added, minor changes

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• Holographic spontaneous anisotropy
• On $\mathcal{N}=1$ susy backgrounds with $AdS$ factor from nonabelian T-duality
• Betti multiplets, flows across dimensions and c-extremization
• AdS${}_5$ black strings in the stu model of FI-gauged $N=2$ supergravity
• $\mathcal{N}=(1,1)$ supersymmetric AdS${}_3$ in 10 dimensions
• Marginal deformations and RG flows for type IIB S-folds
• The symmetric orbifold of N=2 minimal models
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• Chiral Ring of Strange Metals: The Multicolor Limit