Induced fermionic current in AdS spacetime in the presence of a cosmic string and a compactified dimension
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Regular Article - Theoretical Physics
Induced fermionic current in AdS spacetime in the presence of a cosmic string and a compactified dimension S. Bellucci1,a , W. Oliveira dos Santos1,2,b , E. R. Bezerra de Mello2,c 1 2
INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati, Italy Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, PB 58059-900, Brazil
Received: 14 July 2020 / Accepted: 26 September 2020 © The Author(s) 2020
Abstract In this paper, we consider a massive charged fermionic quantum field and investigate the current densities induced by a magnetic flux running along the core of an idealized cosmic string in the background geometry of a 5-dimensional anti-de Sitter spacetime, assuming that an extra dimension is compactified. Along the compact dimension quasi-periodicity condition is imposed on the field with a general phase. Moreover, we admit the presence of a magnetic flux enclosed by the compactified axis. The latter gives rise to Ahanorov–Bohm-like effect on the vacuum expectation value of the currents. In this setup, only azimuthal and axial current densities take place. The former presents two contributions, with the first one due to the cosmic string in a 5-dimensional AdS spacetime without compact dimension, and the second one being induced by the compactification itself. The latter is an odd function of the magnetic flux along the cosmic string and an even function of the magnetic flux enclosed by the compactified axis with period equal to the quantum flux. As to the induced axial current, it is an even function of the magnetic flux along the string’s core and an odd function of the magnetic flux enclosed by the compactification perimeter. For untwisted and twisted field along compact dimension, the axial current vanishes. The massless field case is presented as well some asymptotic limits for the parameters of the model.
1 Introduction In the context of grand unified theories, a consequence of the vacuum symmetry breaking phase transitions is the formation of different types of topological defects in the early Universe [1,2]. In particular, cosmic strings have been receiva e-mail:
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ing considerable attention. Although the recent observational data on the cosmic microwave background (CMB) have ruled out cosmic strings as a primary source for primordial density perturbations, they are still possible candidates for the generation of a variety of interesting physical effects such as gamma ray bursts [3], high energy cosmic rays [4] and gravitational waves [5]. In addition, cosmic strings have also been considered in scenarios beyond the standard model of particles, like in supersymmetry and in string theory approach [6,7]. More recently, the proposal of a formation mechanism for cosmic strings in the framework of brane-inflation has been attracting renewed interest on this type of topological defe
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