Balancing the vacuum energy in heterotic M-theory

Abstract

Moduli stabilisation is explored in the context of low-energy heterotic M -theory to show that a small value of the cosmological constant can result from a balance between the negative potential energy left over from stabilising the moduli and a positive Casimir energy from the higher dimensions. Supersymmetry breaking is induced by the fermion boundary conditions on the two branes in the theory. An explicit calculation of the Casimir energy for the gravitino reveals that the energy has the correct sign, although the size of the contribution is close to the edge of the parameter range for which the calculation is valid.

Electromagnetic Casimir piston in higher-dimensional spacetimes

“…Equation (19) shows that the Casimir force acting between one perfectly conducting plate and one infinitely permeable plate is always repulsive and is a monotonically decreasing function of the distance between the plates. Therefore, in a closed cylinder with finite length, the Casimir force acting on the piston which has different boundary conditions always tends to push the piston to the middle of the cylinder, which is the equilibrium position.…”

“…In the following, we study the asymptotic behavior of the Casimir force (19) at different limits. In the high temperature limit aT ) 1, the Casimir force (19) is dominated by the classical term given by The remaining terms decay exponentially.…”

“…On the one hand, it has been investigated as a candidate for the dark energy that accounts for the accelerated expansion of the Universe [3][4][5][6][7][8][9]. On the other hand, it was studied for its role in the stabilization mechanism of extra dimensions [10][11][12][13][14][15][16][17][18][19].…”

I've Got the World on a Brane

“…The topic of gaugino condensation has received some attention already, as discussed in Section 2.7. It was considered in [36,37] in a much simpler reduction, in which attention was focused on the gravitino and the Calabi-Yau volume modulus. It was found there that the condensate gives a contribution to the flux through the boundary condition on the supergravity three-form and also induces a twist in the chirality condition on the gravitino between the two boundaries.…”

BRST-invariant boundary conditions and strong ellipticity

“…In the 1980's, boundary value problems arose in quantum gravity in connection with the calculation of the Hartle-Hawking wave function of the universe [17], and later they appeared in the theory of strings and branes [9,18,19]. Recently, boundary value problems have featured in the theory of brane cosmology [20] and membranes [21].…”