Abstract
We compute the exact partition function on the branched two-sphere by the localization technique. It is found that it does not depend on a branching parameter q, which means that supersymmetric Rényi entropy defined by utilizing it is equivalent to the usual entanglement entropy. We also provide the interpretation of the conical singularities on the branched sphere as defects sit on the poles of the nonsingular two-sphere.
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References
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
T. Nishioka and I. Yaakov, Supersymmetric Rényi Entropy, JHEP 10 (2013) 155 [arXiv:1306.2958] [INSPIRE].
L.-Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic Calculations of Rényi Entropy, JHEP 12 (2011) 047 [arXiv:1110.1084] [INSPIRE].
X. Huang, S.-J. Rey and Y. Zhou, Three-dimensional SCFT on conic space as hologram of charged topological black hole, JHEP 03 (2014) 127 [arXiv:1401.5421] [INSPIRE].
T. Nishioka, The Gravity Dual of Supersymmetric Rényi Entropy, JHEP 07 (2014) 061 [arXiv:1401.6764] [INSPIRE].
X. Huang and Y. Zhou, \( \mathcal{N}=4 \) super-Yang-Mills on conic space as hologram of STU topological black hole, JHEP 02 (2015) 068 [arXiv:1408.3393] [INSPIRE].
M. Crossley, E. Dyer and J. Sonner, Super-Rényi entropy & Wilson loops for \( \mathcal{N}=4 \) SYM and their gravity duals, JHEP 12 (2014) 001 [arXiv:1409.0542] [INSPIRE].
L.F. Alday, P. Richmond and J. Sparks, The holographic supersymmetric Rényi entropy in five dimensions, JHEP 02 (2015) 102 [arXiv:1410.0899] [INSPIRE].
N. Hama, T. Nishioka and T. Ugajin, Supersymmetric Rényi entropy in five dimensions, JHEP 12 (2014) 048 [arXiv:1410.2206] [INSPIRE].
F. Benini and S. Cremonesi, Partition functions of \( \mathcal{N}=\left(2,2\right) \) gauge theories on S 2 and vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].
N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact results in D = 2 supersymmetric gauge theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].
J. Gomis and S. Lee, Exact Kähler Potential from Gauge Theory and Mirror Symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [INSPIRE].
A. Giveon and D. Kutasov, Supersymmetric Rényi entropy in CFT 2 and AdS 3, JHEP 01 (2016) 042 [arXiv:1510.08872] [INSPIRE].
K. Hosomichi, Orbifolds, Defects and Sphere Partition Function, JHEP 02 (2016) 155 [arXiv:1507.07650] [INSPIRE].
C. Closset and S. Cremonesi, Comments on \( \mathcal{N}=\left(2,2\right) \) supersymmetry on two-manifolds, JHEP 07 (2014) 075 [arXiv:1404.2636] [INSPIRE].
J. Bae, C. Imbimbo, S.-J. Rey and D. Rosa, New Supersymmetric Localizations from Topological Gravity, arXiv:1510.00006 [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
A. Tanaka, Localization on round sphere revisited, JHEP 11 (2013) 103 [arXiv:1309.4992] [INSPIRE].
T. Dimofte, S. Gukov and L. Hollands, Vortex Counting and Lagrangian 3-manifolds, Lett. Math. Phys. 98 (2011) 225 [arXiv:1006.0977] [INSPIRE].
H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A 42 (2009) 504007 [arXiv:0905.2562] [INSPIRE].
T. Okuda, Mirror symmetry and the flavor vortex operator in two dimensions, JHEP 10 (2015) 174 [arXiv:1508.07179] [INSPIRE].
I. Biswas, Parabolic bundles as orbifold bundles, Duke Math. J. 88 (1997) 305.
F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].
F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
G. Clement, Classical solutions in three-dimensional Einstein-Maxwell cosmological gravity, Class. Quant. Grav. 10 (1993) L49 [INSPIRE].
C. Martinez, C. Teitelboim and J. Zanelli, Charged rotating black hole in three space-time dimensions, Phys. Rev. D 61 (2000) 104013 [hep-th/9912259] [INSPIRE].
J.M. Izquierdo and P.K. Townsend, Supersymmetric space-times in (2 + 1) AdS supergravity models, Class. Quant. Grav. 12 (1995) 895 [gr-qc/9501018] [INSPIRE].
E.T. Whittaker and G.N. Watson, A course of modern analysis: an introduction to the general theory of infinite processes and of analytic functions: with an account of the principal transcendental functions, fourth edition, Cambridge University Press, Cambridge U.K. (1927).
K.A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
P. Candelas, X. De La Ossa, A. Font, S.H. Katz and D.R. Morrison, Mirror symmetry for two parameter models. 1., Nucl. Phys. B 416 (1994) 481 [hep-th/9308083] [INSPIRE].
D.R. Morrison and M.R. Plesser, Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties, Nucl. Phys. B 440 (1995) 279 [hep-th/9412236] [INSPIRE].
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Mori, H. Supersymmetric Rényi entropy in two dimensions. J. High Energ. Phys. 2016, 58 (2016). https://doi.org/10.1007/JHEP03(2016)058
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DOI: https://doi.org/10.1007/JHEP03(2016)058