Covariant unification of holographic c-functions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916024633262080 |
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| author | Jokela, Niko Kastikainen, Jani Nunez, Carlos Penín, José Manuel Ruotsalainen, Helime |
| author_facet | Jokela, Niko Kastikainen, Jani Nunez, Carlos Penín, José Manuel Ruotsalainen, Helime |
| contents | We propose a covariant holographic c-function, defined directly in a top-down background and constructed from the extrinsic curvature of codimension-two slices of the bulk geometry. The definition does not rely on a special choice of coordinates or on the existence of a consistent dimensional reduction. We show that it unifies previous foliation-based holographic c-functions into a single covariant formula, reducing to them in the appropriate limits. We evaluate the covariant expression in a range of top-down string backgrounds, including conformal models, confining geometries, flows across dimensions, and the Klebanov-Murugan geometry, in which the holographic radial direction mixes with internal coordinates and which is not the uplift of a lower-dimensional solution. In all cases, the c-function behaves as expected: it interpolates monotonically between AdS fixed points when they are present and decreases towards zero in gapped infrared regions, while in the Klebanov-Murugan case we recover the correct fixed-point values and find evidence for monotonicity. We highlight open conceptual issues, including: the lack of a universal covariant definition of the holographic radial direction in the presence of a nontrivial internal manifold; the derivation of the flow from a bulk action; and the relation to the entanglement c-function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Covariant unification of holographic c-functions Jokela, Niko Kastikainen, Jani Nunez, Carlos Penín, José Manuel Ruotsalainen, Helime High Energy Physics - Theory General Relativity and Quantum Cosmology We propose a covariant holographic c-function, defined directly in a top-down background and constructed from the extrinsic curvature of codimension-two slices of the bulk geometry. The definition does not rely on a special choice of coordinates or on the existence of a consistent dimensional reduction. We show that it unifies previous foliation-based holographic c-functions into a single covariant formula, reducing to them in the appropriate limits. We evaluate the covariant expression in a range of top-down string backgrounds, including conformal models, confining geometries, flows across dimensions, and the Klebanov-Murugan geometry, in which the holographic radial direction mixes with internal coordinates and which is not the uplift of a lower-dimensional solution. In all cases, the c-function behaves as expected: it interpolates monotonically between AdS fixed points when they are present and decreases towards zero in gapped infrared regions, while in the Klebanov-Murugan case we recover the correct fixed-point values and find evidence for monotonicity. We highlight open conceptual issues, including: the lack of a universal covariant definition of the holographic radial direction in the presence of a nontrivial internal manifold; the derivation of the flow from a bulk action; and the relation to the entanglement c-function. |
| title | Covariant unification of holographic c-functions |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.18942 |