Casimir effect in rugby-ball type flux compactifications

Abstract

As a continuation of the work in [1], we discuss the Casimir effect for a massless bulk scalar field in a 4D toy model of a 6D warped flux compactification model, to stabilize the volume modulus. The one-loop effective potential for the volume modulus has a form similar to the Coleman-Weinberg potential. The stability of the volume modulus against quantum corrections is related to an appropriate heat kernel coefficient. However, to make any physical predictions after volume stabilization, knowledge of the derivative of the zeta function, ζ ′ (0) (in a conformally related spacetime) is also required. By adding up the exact mass spectrum using zeta function regularization, we present a revised analysis of the effective potential. Finally, we discuss some physical implications, especially concerning the degree of the hierarchy between the fundamental energy scales on the branes. For a larger degree of warping our new results are very similar to the ones given in Ref [1] and imply a larger hierarchy. In the non-warped (rugby-ball) limit the ratio tends to converge to the same value, independently of the bulk dilaton coupling.

Supersymmetric codimension-two branes in six-dimensional gauged supergravity

“…We will study vacua where the Kalb-Ramond field is consistently (i.e., satisfying its equation of motion) set to zero. Then, the Einstein equations derived from the modified action (31) are…”

Electromagnetic Casimir Effect in AdS Spacetime

“…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]. The case of a brane perpendicular to the AdS boundary is discussed in [21].…”

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

“…In particular, motivated by the problems of the radion stabilization and the cosmological constant generation in braneworld models, the Casimir effect for planar boundaries in antide Sitter space has been widely discussed [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Higherdimensional generalizations of the anti-de Sitter background having compact internal spaces have been considered as well [32][33][34][35][36][37][38][39]. Another class of exactly solvable Casimir problems corresponds to de Sitter spacetime.…”