Abstract:We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.

The entanglement entropy corresponding to a smooth region in general three-dimensional CFTs contains a constant universal term, −F ⊂ SEE. For a disk region, F|disk ≡ F0 coincides with the free energy on 𝕊3 and provides an RG-monotone for general theories. As opposed to the analogous quantity in four dimensions, the value of F generally depends in a complicated (and non-local) way on the geometry of the region and the theory under consideration. For small geometric deformations of the disk in general CFTs as well as for arbitrary regions in holographic theories, it has been argued that F is precisely minimized by disks. Here, we argue that F is globally minimized by disks with respect to arbitrary regions and for general theories. The proof makes use of the strong subadditivity of entanglement entropy and the geometric fact that one can always place an osculating circle within a given smooth entangling region. For topologically non-trivial entangling regions with nB boundaries, the general bound can be improved to F ≥ nBF0. In addition, we provide accurate approximations to F valid for general CFTs in the case of elliptic regions for arbitrary values of the eccentricity which we check against lattice calculations for free fields. We also evaluate F numerically for more general shapes in the so-called “Extensive Mutual Information model”, verifying the general bound.

This article deals with the study of the dynamics of particles in different wormhole geometries. Using the Jacobi metric approach we study the geodesic motion on the Morris–Thorne wormhole. We found the only stable circular orbit located at the throat. We show that the Gaussian curvature of the Jacobi metric is directly related with the wormhole flare-out condition. We provide a simple test for determining the existence of a throat in a spacetime by using the Gaussian curvature of the associated Jacobi metric only. We discuss about the trajectories in the Kepler problem in a wormhole background. Finally, we discuss about the restrictions over the stress–energy tensor imposed by the existence of elliptic orbits in the Kepler problem.

We study the evolution of a Euclidean two-dimensional black hole metric under the second loop renormalization group flow, the RG-2 flow. Since the black hole metric is non-compact (we consider it asymptotically flat) we adapt some proofs for the compact case to the asymptotically flat case. We found that the appearance of horizons during the evolution is related to the parabolicity condition of the flow. We also show that the entanglement entropy of the two-dimensional Euclidean Schwarzschild black hole is monotonic under the RG-2 flow. We generalize the results obtained for the first loop approximation and discuss the implications for higher order loops

In recent years, due to their ability to supply electricity in isolated places where building electrical transmission networks are expensive, Microgrids (MGs) have gained much attention. A new technology called smart inverters (SIs) is currently implemented in inverter-based MGs. SIs are designed to regulate energy under given standards for connecting inverters to the grid. The closed-loop control of SIs technology is still under study and improvement due to several challenges in fields such as stability and reliability. This paper proposes a DQ control for active power regulation on a single-phase voltage source inverter (SPVSI) using a second order sliding mode control (SMC-2) for addressing the abovementioned concerns. The SMC-2 tuning is performed by a metaheuristic algorithm known as particle swarm optimization (PSO). Moreover, to simulate domestic MGs, the SPSVI operation for tracking active power values is performed by ramp rate references based on standard IEEE Std 1547-2018 for inverters connected to the grid. The SMC-2 was appropriately tuned by a PSO algorithm through MATLAB TM and the system simulation through PSCAD TM . The results show that the algorithm performed better compared to a classical algorithm such as proportional-integral control in terms of integral absolute error (IAE) and integral square error (ISE).