De Sitter Vacua and N=2 Supergravity

Author:

Ogetbil, Orcan Bahri

Graduate Program:

Physics

Degree:

Doctor of Philosophy

Document Type:

Dissertation

Date of Defense:

May 05, 2008

Committee Members:

Murat Gunaydin, Committee Chair/Co-Chair
Richard Wallace Robinett, Committee Member
Luen Chau Li, Committee Member
Radu Roiban, Committee Member

Keywords:

N=2
Supergravity
de Sitter
vacua
ground states
cosmological constant
vacuum energy

Abstract:

After reviewing the existing results we give an extensive analysis of the critical points of the potentials of the gauged N = 2 Yang-Mills/Einstein Supergravity theories coupled to tensorand hyper multiplets in five dimensions. Our analysis includes all the possible gaugings of all N = 2 Maxwell-Einstein supergravity theories whose scalar manifolds are symmetric spaces. In general, the scalar potential gets contributions from R-symmetry gauging, tensor couplings and hyper-couplings. We show that the coupling of a hypermultiplet into a theory whose potential has a non-zero value at its critical point, and gauging a compact subgroup of the hyperscalar isometry group will only rescale the value of the potential at the critical point by a positive factor, and therefore will not change the nature of an existing critical point. However this is not the case for non-compact SO(1, 1) gaugings. An SO(1, 1) gauging of the hyper isometry will generally lead to de Sitter vacua, which is analogous to the ground states found by simultaneously gauging SO(1, 1) symmetry of the real scalar manifold of the five dimensional vector multiplets with U(1)R in earlier literature. SO(m, 1) gaugings with m > 1, which give contributions to the scalar potential only in the Magical Jordan family theories, on the other hand, do not lead to de Sitter vacua. Anti-de Sitter vacua are generically obtained when the U(1)R symmetry is gauged. We also show that it is possible to embed certain generic Jordan family theories into the Magical Jordan family while preserving the nature of the ground states. However the Magical Jordan family theories admit additional vacua which are not found in the generic Jordan family theories. The five dimensional stable de Sitter ground states obtained by gauging SO(1, 1) symmetry of the real symmetric scalar manifold (in particular a generic Jordan family manifold of the vector multiplets) simultaneously with a subgroup Rs of the R-symmetry group descend to four dimensional de Sitter ground states under certain conditions. First, the holomorphic section has to be chosen carefully by using the symplectic freedom in four dimensions; and second, a group contraction supported by a rotation of the gauge group generators that carries them into a particular basis is necessary to bring the potential into a desired form. Under this construction, stable de Sitter vacua can be obtained in dimensionally reduced theories (from 5D to 4D) if there is enough freedom to gauge a semi-direct product of SO(1, 1) with R(1,1) together with a simultaneous Rs. We review the stable de Sitter vacua in four dimensions found in earlier literature for N = 2 Yang-Mills Einstein supergravity with SO(2, 1)×Rs gauge group in a symplectic basis that comes naturally after dimensional reduction. Although this particular gauge group does not descend directly from five dimensions, we show that, its contraction does. Hence, two different theories overlap in certain limits. Examples of stable de Sitter vacua are given for the cases: (i) Rs = U(1)R, (ii) Rs = SU(2)R, (iii) N = 2 Yang-Mills/Einstein Supergravity theory coupled to a universal hypermultiplet. These are followed by a discussion regarding the extension of our results to supergravity theories with more general homogeneous scalar manifolds.