Giuseppe Di Giulio, René Meyer, Christian Northe, Henri Scheppach, Suting Zhao
SciPost Phys. Core 6, 049 (2023) ·
published 11 July 2023

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We study the symmetry resolution of the entanglement entropy of an interval in twodimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of extended symmetries such as KacMoody type current algebrae, symmetry resolution is possible only if the boundary conditions on the annulus preserve part of the symmetry group, i.e. if the factorization map associated with the spatial bipartition is compatible with the symmetry in question. The partition function of the boundary CFT (BCFT) is then decomposed in terms of the characters of the irreducible representations of the symmetry group preserved by the boundary conditions. We demonstrate that this decomposition already provides the symmetry resolution of the entanglement spectrum of the corresponding bipartition. Considering the various terms of the partition function associated with the same representation, or charge sector, the symmetryresolved Rényi entropies can be derived to all orders in the UV cutoff expansion without the need to compute the charged moments. We apply this idea to the theory of a free massless boson with $U(1)$, $\mathbb{R}$ and $\mathbb{Z}_2$ symmetry.
Johanna Erdmenger, Bastian Heß, Ioannis Matthaiakakis, René Meyer
SciPost Phys. 14, 099 (2023) ·
published 8 May 2023

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Motivated by establishing holographic renormalization for gravitational theories with nonmetricity and torsion, we present a new and efficient general method for calculating GibbonsHawkingYork (GHY) terms. Our method consists of linearizing any nonlinearity in curvature, torsion or nonmetricity by introducing suitable Lagrange multipliers. Moreover, we use a split formalism for differential forms, writing them in $(n1)+1$ dimensions. The boundary terms of the action are manifest in this formalism by means of Stokes' theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. We observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. Terms polynomial solely in torsion and nonmetricity do not require any GHY term compensation for the variational problem to be welldefined. We test our method by confirming existing results for EinsteinHilbert and fourdimensional ChernSimons modified gravity. Moreover, we obtain new results for torsionful LovelockChernSimons and metricaffine gravity. For all four examples, our new method and results contribute to a new approach towards a systematic hydrodynamic expansion for spin and hypermomentum currents within AdS/CFT.
Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, Jonathan Karl, René Meyer, ZhuoYu Xian
SciPost Phys. 13, 103 (2022) ·
published 3 November 2022

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We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic Poincaré disk, via an inflation rule that allows to construct the tiling using concentric layers of tiles. The models in this class are aperiodic spin chains, whose sequences of couplings are obtained from the bulk inflation rule. We explicitly choose the aperiodic XXZ spin chain with spin 1/2 degrees of freedom as an example. The properties of this model are studied by using strong disorder renormalization group techniques, which provide a tensor network construction for the ground state of this spin chain. This can be regarded as discrete bulk reconstruction. Moreover we compute the entanglement entropy in this setup in two different ways: a discretization of the RyuTakayanagi formula and a generalization of the standard computation for the boundary aperiodic Hamiltonian. For both approaches, a logarithmic growth of the entanglement entropy in the subsystem size is identified. The coefficients, i.e. the effective central charges, depend on the bulk discretization parameters in both cases, albeit in a different way.
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