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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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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.
Free Energy vs SasakiEinstein Volume for Infinite Families of M2Brane Theories
"... Abstract: We investigate infinite families of 3d N = 2 superconformal ChernSimons quivers with an arbitrarily large number of gauge groups arising on M2branes over toric CY4’s. These theories have the same matter content and superpotential of those on D3branes probing cones over La,b,a SasakiEin ..."
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Abstract: We investigate infinite families of 3d N = 2 superconformal ChernSimons quivers with an arbitrarily large number of gauge groups arising on M2branes over toric CY4’s. These theories have the same matter content and superpotential of those on D3branes probing cones over La,b,a SasakiEinstein manifolds. For all these infinite families, we explicitly show the correspondence between the free energy F on S3 and the volume of the 7dimensional base of the associated CY4, even before extremization. Our results add to those existing in the literature, providing further support for the correspondence. We develop a lifting algorithm, based on the Type IIB realization of these theories, that takes from CY3’s to CY4’s and we use it to efficiently generate the models studied in the paper. We also introduce a procedure, based on the mapping between extremal points in the toric diagram (GLSM fields) and chiral fields in the quiver, which systematically translates symmetries of the toric diagram into constraints of the trial Rcharges of the quiver, beyond those arising from marginality of the superpotential. This method can be exploited for reducing the dimension of the space of trial Rcharges over which the free energy is maximized. Finally, we show that in all the
Anomalous dimensions of monopole operators in threedimensional quantum electrodynamics
"... The space of local operators in threedimensional quantum electrodynamics contains monopole operators that create n units of gauge flux emanating from the insertion point. This paper uses the stateoperator correspondence to calculate the anomalous dimensions of these monopole operators perturbative ..."
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The space of local operators in threedimensional quantum electrodynamics contains monopole operators that create n units of gauge flux emanating from the insertion point. This paper uses the stateoperator correspondence to calculate the anomalous dimensions of these monopole operators perturbatively to nexttoleading order in the 1/Nf expansion, thus improving on the existing leading order results in the literature. Here, Nf is the number of twocomponent complex fermion flavors. The scaling dimension of the n = 1 monopole operator is 0.265Nf − 0.0383 +O(1/Nf) at the infrared conformal fixed point.
PUPT2440 On RG Flow of τRR for Supersymmetric Field Theories in ThreeDimensions
"... The coefficient τRR of the twopoint function of the superconformal U(1)R currents of N = 2 SCFTs in threedimensions is recently shown to be obtained by differentiating the partition function on a squashed threesphere with respect to the squashing parameter. With this method, we compute the τRR fo ..."
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The coefficient τRR of the twopoint function of the superconformal U(1)R currents of N = 2 SCFTs in threedimensions is recently shown to be obtained by differentiating the partition function on a squashed threesphere with respect to the squashing parameter. With this method, we compute the τRR for N = 2 WessZumino models and SQCD numerically for small number of flavors and analytically in the large number limit. We study the behavior of τRR under an RG flow by adding superpotentials to the theories. While the τRR decreases for the gauge theories, we find an N = 2 WessZumino model whose τRR increases along the RG flow. Since τRR is proportional to the coefficient CT of the twopoint correlation function of the stressenergy tensors for N = 2 superconformal field theories, this rules out the possibility of CT being a measure of the degrees of freedom which monotonically decreases along RG flows in threedimensions.
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"... A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is welldefined ..."
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A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is welldefined with respect to the relevant coupling, 2) the entropy is stationary, but the perturbation fails, 3) the entropy is neither stationary nor perturbative. We compare our holographic results with the numerical calculation for a free massive scalar field in threedimensions, and find a qualitative agreement between them. We speculate that these statements hold for any relevant perturbation in any quantum field theory invariant under the Poincare ́ symmetry.
Monopole Taxonomy in ThreeDimensional Conformal Field Theories
"... We study monopole operators at the infrared fixed points of Abelian and nonAbelian gauge theories with Nf fermion flavors in three dimensions. At large Nf, independent monopole operators can be defined via the stateoperator correspondence only for stable monopole backgrounds. In Abelian theories, ..."
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We study monopole operators at the infrared fixed points of Abelian and nonAbelian gauge theories with Nf fermion flavors in three dimensions. At large Nf, independent monopole operators can be defined via the stateoperator correspondence only for stable monopole backgrounds. In Abelian theories, every monopole background is stable. In the nonAbelian case, we find that many (but not all) backgrounds are stable in each topological class. We calculate the infrared scaling dimensions of the corresponding operators through nexttoleading order in 1/Nf. In the case of U(Nc) QCD with Nf fundamental fermions (and in particular in the QED case, Nc = 1), we find that the monopole operators transform as nontrivial irreducible representations of the SU(Nf) flavor symmetry group. ar X iv