## DSpace/Manakin Repository

 Title: Rényi Entropies for Free Field Theories Author: Klebanov, Igor R.; Pufu, Silviu S.; Sachdev, Subir; Safdi, Benjamin R. Note: Order does not necessarily reflect citation order of authors. Citation: Klebanov, Igor R., Silviu S. Pufu, Subir Sachdev, and Benjamin R. Safdi. 2012. Rényi entropies for free field theories. Journal of High Energy Physics 2012:74. Full Text & Related Files: Sachdev_Renyi.pdf (626.2Kb; PDF) Abstract: Rényi entropies $$S_{q}$$ are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with $$q \geq 0$$. For $$(d + 1)$$-dimensional conformal field theories, the Rényi entropies across $$S^{d−1}$$ may be extracted from the thermal partition functions of these theories on either $$(d + 1)$$-dimensional de Sitter space or $$\mathbb{R} \times \mathbb{H}^{d}$$, where $$\mathbb{H}^{d}$$ is the d-dimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the $$(d + 1)$$-dimensional sphere and $$S^{1} \times \mathbb{H}^{d}$$, respectively. We calculate the Rényi entropies of free massless scalars and fermions in d = 2, and show how using zeta-function regularization one finds agreement between the calculations on the branched coverings of $$S^{3}$$ and on $$S^{1} \times \mathbb{H}^{2}$$. Analogous calculations for massive free fields provide monotonic interpolating functions between the Rényi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Rényi entropy calculations in $$d > 2$$. Published Version: doi:10.1007/JHEP04(2012)074 Other Sources: http://arxiv.org/abs/1111.6290 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10860096 Downloads of this work: