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arXiv:2004.06981 · The European Physical Journal C

Left-right entanglement entropy for a Dp-brane with dynamics and background fields

Shirin Teymourtashlou, Davoud Kamani

Published Apr 1, 2020• 3 citations
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Abstract

Abstract We investigate the left-right entanglement entropy of a boundary state, corresponding to a dynamical Dp-brane with the internal and background fields. We assume that the brane has a tangential linear motion and a rotation, and is dressed with an internal U(1) gauge potential and the Kalb–Ramond tensor field $$B_{\mu \nu }$$ Bμν . We derive the entanglement entropy via the Rényi entropy by applying the replica trick. Our calculations will be in the context of the bosonic string theory.

DOI
10.1140/epjc/s10052-020-7883-0

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Abstract We investigate the left-right entanglement entropy of a boundary state, corresponding to a dynamical Dp-brane with the internal and background fields. We assume that the brane has a tangential linear motion and a rotation, and is dressed with an internal U(1) gauge potential and the Kalb–Ramond tensor field BμνB_{\mu \nu }Bμν​ Bμν . We derive the entanglement entropy via the Rényi entropy by applying the replica trick. Our calculations will be in the context of the bosonic string theory.
We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.
A bstract In the context of the type IIA/IIB superstring theories, we derive the left-right entanglement entropy (LREE) of a BPS D p -brane with transverse motion in the presence of a U(1) gauge potential and the Kalb-Ramond field in the partially compact spacetime T n ⊗ ℝ 1,9 − n . At first we employ the replica trick to compute the Rényi entropy and then we obtain the entanglement entropy. We examine the results for the special case, i.e. for the D6-brane. Besides, we investigate the thermodynamical entropy, associated with the LREE. This demonstrates that the LREE is precisely equivalent to its thermodynamic counterpart.
Abstract We obtain the left-right entanglement entropy (LREE) for a Dp-brane with tangential motion in the presence of a U(1) gauge potential, the Kalb–Ramond field and an open string tachyon field. Thus, at first we extract the Rényi entropy and then by taking a special limit of it we acquire the entanglement entropy. We shall investigate the behavior of the LREE under the tachyon condensation phenomenon. We observe that the deformation of the LREE, through this process, reveals the collapse of the brane. Besides, we examine the second law of thermodynamics for the LREE under tachyon condensation, and we extract the imposed constraints. Note that our calculations will be in the context of the type IIA/IIB superstring theories.
We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.
We derive the left-right entanglement entropy (LREE) for a bosonic Dp-brane. This brane has tangential dynamics and has been dressed by a U(1) gauge potential, the Kalb-Ramond field and a tachyon field. For this purpose, the Rényi entropy will be computed and then, by taking a special limit of it, the LREE will be obtained. Besides, the behavior of the LREE under the tachyon condensation process will be evaluated. In addition, after the transition of the system, i.e. the collapse of the unstable brane, the second law of the thermodynamics on the LREE will be checked. We find that preserving the second law imposes some conditions on the parameters of the setup.
We study the entanglement entropy for open bosonic strings on multiple Dp -branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which Dp -branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of ( p − 1 ) -dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) region. However, the leading divergences are mainly due to tachyon contributions to the entanglement entropy, which may be absent in supersymmetric string theories . Apart from the divergences thanks to tachyons, the entanglement entropy for open bosonic strings on Dp -branes is finite for 2 ≤ p ≤ d critical − 2 and logarithmically divergent for p = 1 , d critical − 1 .