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Rényi Entropies for Free Field Theories
"... Rényi entropies Sq are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q ≥ 0. For (d + 1)dimensional conformal field theories, the Rényi entropies across Sd−1 may be extracted from the thermal partition functions of ..."
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Cited by 16 (2 self)
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Rényi entropies Sq are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q ≥ 0. For (d + 1)dimensional conformal field theories, the Rényi entropies across Sd−1 may be extracted from the thermal partition functions of these theories on either (d+1)dimensional de Sitter space or R×Hd, where Hd is the ddimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the (d+ 1)dimensional sphere and S1 × Hd, respectively. We calculate the Rényi entropies of free massless scalars and fermions in d = 2, and show how using zetafunction regularization one finds agreement between the calculations on the branched coverings of S3 and on S1 × H2. 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.
Rigidly supersymmetric gauge theories on curved superspace
 JHEP
, 2012
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Nonlinear sigma models with AdS supersymmetry in three dimensions
, 2012
"... In threedimensional antide Sitter (AdS) space, there exist several realizations of Nextended supersymmetry, which are traditionally labelled by two nonnegative integers p ≥ q such that p + q = N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target sp ..."
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Cited by 8 (6 self)
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In threedimensional antide Sitter (AdS) space, there exist several realizations of Nextended supersymmetry, which are traditionally labelled by two nonnegative integers p ≥ q such that p + q = N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target space geometry of supersymmetric nonlinear σmodels. We classify all possible types of hyperkähler target spaces for the cases N = 3 and N = 4 by making use of two different realizations for the most general (p, q) supersymmetric σmodels: (i) offshell formulations in terms of N = 3 and N = 4 projective supermultiplets; and (ii) onshell formulations in terms of covariantly chiral scalar superfields in (2,0) AdS superspace. Depending on the type of N = 3, 4 AdS supersymmetry, nonlinear σmodels can support one of the following target space geometries: (i) hyperkähler cones; (ii) noncompact hyperkähler manifolds with a U(1) isometry group which acts nontrivially on the twosphere of complex structures; (iii) arbitrary hyperkähler manifolds including compact ones. The option (iii) is realized only in the case of critical (4,0) AdS supersymmetry. As an application of the (4,0) AdS techniques developed, we also construct the most general nonlinear σmodel in Minkowski space with a noncentrally extended N = 4 Poincare ́ supersymmetry. Its target space is a hyperkähler cone (which is characteristic of N = 4 superconformal σmodels), but the σmodel is massive. The Lagrangian includes a positive potential constructed in terms of the homothetic conformal Killing vector the target space is endowed with. This mechanism of mass generation differs from the standard one which corresponds to a σmodel with the ordinary N = 4 Poincare ́ supersymmetry and which makes use of a triholomorphic Killing vector. ar
Elliptic hypergeometric integrals and ’t Hooft anomaly matching conditions
 JHEP 1206 (2012) 016, arXiv:1203.5677 [hepth
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Symmetries of curved superspace
 JHEP
, 2013
"... The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N = 1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgro ..."
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The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N = 1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgrounds associated with any supergravity theory formulated in superspace. In particular, it has already been used to construct rigid supersymmetric field theories in 5D N = 1, 4D N = 2 and 3D (p, q) antide Sitter superspaces. In the last two years, there have appeared a number of publications devoted to the construction of supersymmetric backgrounds in offshell 4D N = 1 supergravity theories using component field considerations. Here we demonstrate how to read off the key results of these recent publications from the more general superspace approach developed in the 1990s. We also present a universal superspace setting to construct supersymmetric backgrounds, which is applicable to any of the known offshell formulations for N = 1 supergravity. This approach is based on the realizations of the new minimal and nonminimal supergravity theories as superWeyl invariant couplings of the old minimal supergravity to certain conformal compensators. ar
Modified elliptic gamma functions and 6d superconformal indices,” arXiv:1211.2703 [hepth
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Extended supersymmetric sigma models in AdS4 from projective superspace
, 2012
"... There exist two superspace approaches to describe N = 2 supersymmetric nonlinear σmodels in fourdimensional antide Sitter (AdS4) space: (i) in terms of N = 1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms ofN = 2 polar supermultiplets using the AdS ..."
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There exist two superspace approaches to describe N = 2 supersymmetric nonlinear σmodels in fourdimensional antide Sitter (AdS4) space: (i) in terms of N = 1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms ofN = 2 polar supermultiplets using the AdS projectivesuperspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N = 2 supersymmetric σmodels in AdS4. The target space must be a noncompact hyperkähler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the twosphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkähler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N = 1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N = 2 supersymmetric nonlinear σmodel in AdS4 in terms of chiral superfields on threedimensional N = 2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the fourdimensional N = 2 AdS superspace that makes use of Poincare ́ coordinates for AdS4. This novel formulation allows us to uncover several interesting geometric results. ar
Coupling of the BLG theory to a conformal supergravity background
 JHEP 1301, 120 (2013) [arXiv:1206.5388 [hepth
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