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Register a new userEntanglement, anomalies and Mathissons helices
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Added by
Alvaro Veliz-Osorio
Publication date
2018
fields
Physics
and research's language is
English
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We study the physical properties of a length-torsion functional which encodes the holographic entanglement entropy for 1+1 dimensional theories with chiral anomalies. Previously, we have shown that its extremal curves correspond to the mysterious Mathissons helical motions for the centroids of spinning bodies. We explore the properties of these helices in domain-wall backgrounds using both analytic and numerical techniques. Using these insights we derive an entropic $c$-function $c_{mathrm{Hel}}(ell)$ which can be succinctly expressed in terms of Noether charges conserved along these helical motions. While for generic values of the anomaly there is some ambiguity in the definition of $c_{mathrm{Hel}}(ell)$, we argue that at the chiral point this ambiguity is absent.
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We study extremal curves associated with a functional which is linear in the curves torsion. The functional in question is known to capture the properties of entanglement entropy for two-dimensional conformal field theories with chiral anomalies and has potential applications in elucidating the equilibrium shape of elastic linear structures. We derive the equations that determine the shape of its extremal curves in general ambient spaces in terms of geometric quantities. We show that the solutions to these shape equations correspond to a three-dimensional version of Mathissons helical motions for the centers of mass of spinning probes. Thereafter, we focus on the case of maximally symmetric spaces, where solutions correspond to cylindrical helices and find that the Lancret ratio of these equals the relative speed between the Mathisson-Pirani and the Tulczyjew-Dixon observers. Finally, we construct all possible helical motions in three-dimensional manifolds with constant negative curvature. In particular, we discover a rich space of helices in AdS$_3$ which we explore in detail.
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Hawking radiation is obtained from anomalies resulting from a breaking of diffeomorphism symmetry near the event horizon of a black hole. Such anomalies, manifested as a nonconservation of the energy momentum tensor, occur in two different forms -- covariant and consistent. The crucial role of covariant anomalies near the horizon is revealed since this is the {it only} input required to obtain the Hawking flux, thereby highlighting the universality of this effect. A brief description to apply this method to obtain thermodynamic entities like entropy or temperature is provided.
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