On entanglement c-functions in confining gauge field theories
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arXiv
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| Format: | Preprint |
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2025
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| author | Jokela, Niko Kastikainen, Jani Nunez, Carlos Penín, José Manuel Ruotsalainen, Helime Subils, Javier G. |
| author_facet | Jokela, Niko Kastikainen, Jani Nunez, Carlos Penín, José Manuel Ruotsalainen, Helime Subils, Javier G. |
| contents | Entanglement entropy has proven to be a powerful tool for probing renormalization group (RG) flows in quantum field theories, with c-functions derived from it serving as candidate measures of the effective number of degrees of freedom. While the monotonicity of such c-functions is well established in many settings, notable exceptions occur in theories with a mass scale. In this work, we investigate entanglement c-functions in the context of holographic RG flows, with a particular focus on flows across dimensions induced by circle compactifications. We argue that in spacetime dimensions $d \geq 4$, standard constructions of c-functions, which rely on higher derivatives of the entanglement entropy of either a ball or a cylinder, generically lead to non-monotonic behavior. Working with known dual geometries, we argue that the non-monotonicity stems not from any pathology or curvature singularity, but from a transition in the holographic Ryu--Takayanagi surface. In compactifications from four to three dimensions, we propose a modified construction that restores monotonicity in the infrared, although a fully monotonic ultraviolet extension remains elusive. Furthermore, motivated by entanglement entropy inequalities, we conjecture a bound on the cylinder entanglement c-function, which holds in all our examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On entanglement c-functions in confining gauge field theories Jokela, Niko Kastikainen, Jani Nunez, Carlos Penín, José Manuel Ruotsalainen, Helime Subils, Javier G. High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology Entanglement entropy has proven to be a powerful tool for probing renormalization group (RG) flows in quantum field theories, with c-functions derived from it serving as candidate measures of the effective number of degrees of freedom. While the monotonicity of such c-functions is well established in many settings, notable exceptions occur in theories with a mass scale. In this work, we investigate entanglement c-functions in the context of holographic RG flows, with a particular focus on flows across dimensions induced by circle compactifications. We argue that in spacetime dimensions $d \geq 4$, standard constructions of c-functions, which rely on higher derivatives of the entanglement entropy of either a ball or a cylinder, generically lead to non-monotonic behavior. Working with known dual geometries, we argue that the non-monotonicity stems not from any pathology or curvature singularity, but from a transition in the holographic Ryu--Takayanagi surface. In compactifications from four to three dimensions, we propose a modified construction that restores monotonicity in the infrared, although a fully monotonic ultraviolet extension remains elusive. Furthermore, motivated by entanglement entropy inequalities, we conjecture a bound on the cylinder entanglement c-function, which holds in all our examples. |
| title | On entanglement c-functions in confining gauge field theories |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2505.14397 |