Abstract
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.
Highlights
By applying the boundary state formalism, our goal is to investigate a special property of the D-branes, which is called left-right entanglement entropy (LREE) [16]-[19]
We figure out the LREE of a bosonic unstable Dp-brane with a tangential linear motion and rotation which has been dressed by the Kalb-Ramond field, a U(1) gauge potential and a tachyon field of the open string spectrum
Since the open string tachyon field lives on our brane we were motivated to investigate effect of the tachyon condensation on the LREE corresponding to our unstable brane
Summary
The entanglement entropy, as an appropriate measure for entanglement, has been widely studied in the different contexts. By applying the boundary state formalism, our goal is to investigate a special property of the D-branes, which is called left-right entanglement entropy (LREE) [16]-[19]. Since the open string tachyon field lives on our brane we were motivated to investigate effect of the tachyon condensation on the LREE corresponding to our unstable brane. The corresponding LREE of a D-brane potentially possesses a connection with the entropies of the black holes [3, 4]. Quiroz for a onedimensional boundary state in a 2D CFT with the Dirichlet or the Neumann boundary condition [16] They extended their work to the case of a bare-stationary Dp-brane [17]. We shall apply their approach to compute the LREE of our setup.
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