Stress-energy tensor induced by a bulk Dirac spinor in the Randall-Sundrum model

Abstract

Motivated by the possible extension into a supersymmetric Randall-Sundrum (RS) model, we investigate the properties of the vacuum expectation value (VEV) of the stress-energy tensor for a quantized bulk Dirac spinor field in the RS geometry and compare it with that for a real scalar field. This is carried out via the Green function method based on first principles without invoking the degeneracy factor, whose validity in a warp geometry is a priori unassured. In addition, we investigate the local behavior of the Casimir energy near the two branes. One salient feature we found is that the surface divergences near the two branes have opposite signs. We argue that this is a generic feature of the fermionic Casimir energy density due to its parity transformation in the fifth dimension. Furthermore, we investigate the self-consistency of the RS metric under the quantum correction due to the stress-energy tensor. It is shown that the VEV of the stress-energy tensor and the classical one become comparable near the visible brane if k M M P l (the requirement of no hierarchy problem), where k is the curvature of the RS warped geometry and M the 5-dimensional Planck mass. In that case the self-consistency of RS model that includes bulk fields is in doubt. If, however, k M , then an approximate self-consistency of the RS-type metric may still be satisfied.

Electromagnetic Casimir Effect in AdS Spacetime

“…In addition to describing the physical structure of the quantum field at a given point, this VEV acts as the source in the Einstein equations and therefore plays an important role in modelling a self-consistent dynamics involving the gravitational field. The VEV of the energy-momentum tensor for scalar and fermionic fields in the geometry of two branes parallel to the AdS boundary has been investigated in [5][6][7][8][9][10]. Both the global and local characteristics in higher-dimensional generalizations of the AdS spacetime with compact internal spaces are studied in [11][12][13][14][15][16][17][18][19][20].…”

Quantum Vacuum Effects in Braneworlds on AdS Bulk

“…In addition, the quantum effects of bulk fields generate a cosmological constant on the brane. Motivated by these points, the Casimir effect in braneworld models on the AdS bulk, with branes parallel to the AdS boundary, has been investigated for scalar [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], fermionic [39][40][41][42][43] and vector fields [44][45][46][47][48][49]. The models with de Sitter branes have been discussed in [50][51][52][53][54][55][56][57][58].…”

“…The Casimir densities for a Z 2 -symmetric thick brane for the general case of static plane symmetric interior structure have been discussed in [68]. The VEVs of the energy-momentum tensor for Dirac spinor field and for the electromagnetic field are investigated in [42,43,[46][47][48][49]. The geometry of a brane intersecting the AdS boundary is considered in [69].…”

Quantum vacuum effects in braneworlds on AdS bulk

“…The Casimir densities for a Z 2 -symmetric thick brane for the general case of static plane symmetric interior structure have been discussed in [17]. The VEVs of the energy-momentum tensor for Dirac spinor field and for the electromagnetic field are investigated in [18,19] and [13,20,21,22]. The geometry of a brane intersecting the AdS boundary has been considered in [23].…”