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Register a new userCasimir force in brane worlds: coinciding results from Greens and Zeta function approaches
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Casimir force encodes the structure of the field modes as vacuum fluctuations and so it is sensitive to the extra dimensions of brane worlds. Now, in flat spacetimes of arbitrary dimension the two standard approaches to the Casimir force, Greens function and zeta function, yield the same result, but for brane world models this was only assumed. In this work we show both approaches yield the same Casimir force in the case of Universal Extra Dimensions and Randall-Sundrum scenarios with one and two branes added by p compact dimensions. Essentially, the details of the mode eigenfunctions that enter the Casimir force in the Greens function approach get removed due to their orthogonality relations with a measure involving the right hyper-volume of the plates and this leaves just the contribution coming from the Zeta function approach. The present analysis corrects previous results showing a difference between the two approaches for the single brane Randall-Sundrum; this was due to an erroneous hyper-volume of the plates introduced by the authors when using the Greens function. For all the models we discuss here, the resulting Casimir force can be neatly expressed in terms of two four dimensional Casimir force contributions: one for the massless mode and the other for a tower of massive modes associated with the extra dimensions.
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In looking for imprints of extra dimensions in brane world models one usually builts these so that they are compatible with known low energy physics and thus focuses on high energy effects. Nevertheless, just as submillimeter Newtons law tests probe the mode structure of gravity other low energy tests might apply to matter. As a model example, in this work we determine the 4D Casimir force corresponding to a scalar field subject to Dirichlet boundary conditions on two parallel planes lying within the single brane of a Randall-Sundrum scenario extended by one compact extra dimension. Using the Greens function method such a force picks the contribution of each field mode as if it acted individually but with a weight given by the square of the mode wave functions on the brane. In the low energy regime one regains the standard 4D Casimir force that is associated to a zero mode in the massless case or to a quasilocalized or resonant mode in the massive one whilst the effect of the extra dimensions gets encoded as an additional term.
We show that contrary to first expectations realistic three generation supersymmetric intersecting brane world models give rise to phenomenologically interesting predictions about gauge coupling unification. Assuming the most economical way of realizing the matter content of the MSSM via intersecting branes we obtain a model independent relation among the three gauge coupling constants at the string scale. In order to correctly reproduce the experimentally known values of sin^2[theta_W(M_z)] and alpha_s(M_z) this relation leads to natural gauge coupling unification at a string scale close to the standard GUT scale 2 x 10^16 GeV. Additional vector-like matter can push the unification scale up to the Planck scale.
We present the fundamental techniques and working equations of many-body Greens function theory for calculating ground state properties and the spectral strength. Greens function methods closely relate to other polynomial scaling approaches discussed in chapters 8 and 10. However, here we aim directly at a global view of the many-fermion structure. We derive the working equations for calculating many-body propagators, using both the Algebraic Diagrammatic Construction technique and the self-consistent formalism at finite temperature. Their implementation is discussed, as well as the inclusion of three-nucleon interactions. The self-consistency feature is essential to guarantee thermodynamic consistency. The pairing and neutron matter models introduced in previous chapters are solved and compared with the other methods in this book.
We clarify the relation between orbifold and interval pictures in 5d brane worlds. We establish this correspondence for Z_2-even and Z_2-odd orbifold fields. In the interval picture Gibbons-Hawking terms are necessary to fulfill consistency conditions. We show how the brane world consistency conditions arise in the interval picture. We apply the procedure to the situation where the transverse dimension is terminated by naked singularities. In particular, we find the boundary terms needed when the naive vacuum action is infinite.
Depending on the point of view, the Casimir force arises from variation in the energy of the quantum vacuum as boundary conditions are altered or as an interaction between atoms in the materials that form these boundary conditions. Standard analyses of such configurations are usually done in terms of ordinary, equal-time (Minkowski) coordinates. However, physics is independent of the coordinate choice, and an analysis based on light-front coordinates, where $x^+equiv t+z/c$ plays the role of time, is equally valid. After a brief historical introduction, we illustrate and compare equal-time and light-front calculations of the Casimir force.
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