Pierre Ramond
Contribution to the Peter Freund Memorial volume: a glossary of group-theoretic facts that may relate the seven-dimensional Freund-Rubin coset to Yukawa textures.
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We utilise the duality between M theory and Type IIA string theory to show the existence of Freund-Rubin compactifications of M theory on 7-manifolds with singularities supporting chiral fermions. This leads to a concrete way to study phenomenologically interesting quantum gravity vacua using a holographically dual three dimensional field theory.
We discuss the effective action for weak G_2 compactifications of M-theory. The presence of fluxes acts as a source for the the axions and drives the Freund-Rubin parameter to zero. The result is a stable non-supersymmetric vacuum with a negative cosmological constant. We also give the superpotential which generates the effective potential and discuss a simple model which aims to incorporate the effects of supersymmetry breaking by the gauge sector.
In the $n-$dimensional Freund-Rubin model with an antisymmetric tensor field of rank $s-1$, the dimension of the external spacetime we live in must be $min(s, n-s)$. This result is a generalization of the previous result in the $d=11$ supergravity case, where $s = 4$.
We investigate stability of two branches of Freund-Rubin compactification from thermodynamic and dynamical perspectives. Freund-Rubin compactification allows not only trivial solutions but also warped solutions describing warped product of external de Sitter space and internal deformed sphere. We study dynamical stability by analyzing linear perturbations around solutions in each branch. Also we study thermodynamic stability based on de Sitter entropy. We show complete agreement of thermodynamic and dynamical stabilities of this system. Finally, we interpret the results in terms of effective e…
We discuss the Freund-Rubin compactification with cosmological constant and the dilaton field, and examine the stability of the spacetimes at the low energy. The Minkowski or de Sitter spacetime can be obtained if the dilation field is turned off while we observe that the dilaton field does not permit such spacetimes but only the anti-de Sitter spacetime. The stability of the spacetime depends on the dimensions of the spacetime and the compactified space and the coupling constant of the dilaton field $a$. In the $a=1$ case, which corresponds to superstring theories, the anti-de Sitter vacuum i…
You've got a Freund--Rubin in Me: The Aretakis Instability of Extremal Black Branes
本研究聚焦近视界几何，发现Aretakis不稳定性强度由近视界AdS_{p+2}因子的标度维数决定，等价于计算Freund--Rubin空间的Kaluza--Klein谱，论证非膨胀极端黑膜受此不稳定性且弱于极端黑洞，还揭示标度维数对形变光滑性的影响。
In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund-Rubin backgrounds, and propose a geometric construction extending the well-known construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but tha…
We study the stability of Freund-Rubin compactifications, AdS_p x M_q, of p+q-dimensional gravity theories with a q-form field strength and no cosmological term. We show that the general AdS_p x S^q vacuum is classically stable against small fluctuations, in the sense that all modes satisfy the Breitenlohner-Freedman bound. In particular, the compactifications used in the recent discussion of the proposed bosonic M-theory are perturbatively stable. Our analysis treats all modes arising from the graviton and the q-form, and is completely independent of supersymmetry. From the masses of the line…
We consider the Freund-Rubin-Englert mechanism of compactification of N=1 supergravity in 11 dimensions. We systematically investigate both well-known and some new solutions of the classical equations of motion in 11 dimensions. In particular, we show that any threeform potential in 11 dimension is given locally by the structure constants of a geodesic loop in an affinely connected space.
We found a new branch of solutions in Freund-Rubin type flux compactifications. The geometry of these solutions is described as the external space which has a de Sitter symmetry and the internal space which is topologically spherical. However, it is not a simple form of dS_p x S^q but a warped product of de Sitter space and a deformed sphere. We explicitly constructed numerical solutions for a specific case with p=4 and q=4. We show that the new branch of solutions emanates from the marginally stable solution in the branch of dS_4 x S^4 solutions.
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