Holographic interpolation between a and F
| Autor: | Tatsuma Nishioka, Teruhiko Kawano, Yuki Nakaguchi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Physics
High Energy Physics - Theory Nuclear and High Energy Physics Conjecture Analytic continuation Dimension (graph theory) FOS: Physical sciences Monotonic function Function (mathematics) Space (mathematics) Flow (mathematics) High Energy Physics - Theory (hep-th) Interpolation Mathematical physics |
| Zdroj: | Journal of High Energy Physics |
| Popis: | An interpolating function $\tilde F$ between the $a$-anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization group flow in continuous dimension $d$. We examine $\tilde F$ in the large-$N$ CFT's in $d$ dimensions holographically described by the Einstein-Hilbert gravity in the AdS$_{d+1}$ space. We show that $\tilde F$ is a smooth function of $d$ and correctly interpolates the $a$ coefficients and the free energies. The monotonicity of $\tilde F$ along an RG flow follows from the analytic continuation of the holographic $c$-theorem to continuous $d$, which completes the proof of the conjecture. 3 pages, v2: a reference added, minor changes |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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