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We present a brane-world scenario in which two regions of $AdS_5$ space-time are glued together along a 3-brane with constant positive curvature such that {em all} spatial dimensions form a compact manifold of topology $S^4$. It turns out that the induced geometry on the brane is given by Einsteins static universe. It is possible to achieve an anisotropy of the manifold which allows for a huge hierarchy between the size of the extra dimension $R$ and the size of the observable universe $R_U$ at present. This anisotropy is also at the origin of a very peculiar property of our model: the physical distance between {em any two points} on the brane is of the order of the size of the extra dimension $R$ regardless of their distance measured with the use of the induced metric on the brane. In an intermediate distance regime $R ll r ll R_U$ gravity on the brane is shown to be effectively 4-dimensional, with corresponding large distance corrections, in complete analogy with the Randall-Sundrum II model. For very large distances $r sim R_U$ we recover gravity in Einsteins static universe. However, in contrast to the Randall-Sundrum II model the difference in topology has the advantage of giving rise to a geodesically complete space.
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We consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman-Bondi Universe where the origin of space plays a special role. The embedding is chosen such that the induced matter distribution on the brane respects the spherical symmetry of matter in the extra dimensional space. The mirage cosmology on the probe brane is studied, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We then focus on the spatial geometry around the origin and show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann-Lemaitre 4d space-time. For instance, when a 3-brane is embedded in a 5d matter dominated model, the 4d dynamics around the origin converge to a Friedmann-Lemaitre Universe in a radiation dominated epoch. We analyse this isotropisation process and show that it is a late time attractor.
Since the dawn of the new millennium, there has been a revived interest in the concept of extra dimensions.In this scenario all the standard model matter and gauge fields are confined to the 4 dimensions and only gravity can escape to higher dimensions of the universe.This idea can be tested using table-top experiments, collider experiments, astrophysical or cosmological observations. The main astrophysical constraints come from the cooling rate of supernovae, neutron stars, red giants and the sun. In this article, we consider the energy loss mechanism of SN1987A and study the constraints it places on the number and size of extra dimensions and the higher dimensional Planck scale.
We show that the strong CP problem can, in principle, be solved dynamically by adding extra-dimensions with compact topology. To this aim we consider a toy model for QCD, which contains a vacuum angle and a strong CP like problem. We further consider a higher dimensional theory, which has a trivial vacuum structure and which reproduces the perturbative properties of the toy model in the low-energy limit. In the weak coupling regime, where our computations are valid, we show that the vacuum structure of the low-energy action is still trivial and the strong CP problem is solved. No axion-like particle occur in this setup and therefore it is not ruled out by astrophysical bounds.
We consider a real scalar field with an arbitrary negative bulk mass term in a general 5D setup, where the extra spatial coordinate is a warped interval of size $pi R$. When the 5D field verifies Neumann conditions at the boundaries of the interval, the setup will always contain at least one tachyonic KK mode. On the other hand, when the 5D scalar verifies Dirichlet conditions, there is always a critical (negative) mass $M_{c}^2$ such that the Dirichlet scalar is stable as long as its (negative) bulk mass $mu^2$ verifies $M^2_{c}<mu^2$. Also, if we fix the bulk mass $mu^2$ to a sufficiently negative value, there will always be a critical interval distance $pi R_c$ such that the setup is unstable for $R>R_c$. We point out that the best mass (or distance) bound is obtained for the Dirichlet BC case, which can be interpreted as the generalization of the Breitenlohner-Freedman (BF) bound applied to a general compact 5D warped spacetime. In particular, in a slice of $AdS_5$ the critical mass is $M^2_{c}=-4k^2 -1/R^2$ and the critical interval distance is given by $1/R_c^2=|mu^2|-4k^2$, where $k$ is the $AdS_5$ curvature (the 5D flat case can be obtained in the limit $kto 0$, whereas the infinite $AdS_5$ result is recovered in the limit $Rto infty$).
What is the dimension of spacetime? We address this question in the context of the AdS/CFT Correspondence. We give a prescription for computing the number of large bulk dimensions, $D$, from strongly-coupled CFT$_d$ data, where large means parametrically of order the AdS scale. The idea is that unitarity of 1-loop AdS amplitudes, dual to non-planar CFT correlators, fixes $D$ in terms of tree-level data. We make this observation rigorous by deriving a positive-definite sum rule for the 1-loop double-discontinuity in the flat space/bulk-point limit. This enables us to prove an array of AdS/CFT folklore, and to infer new properties of large $N$ CFTs at strong coupling that ensure consistency of emergent large extra dimensions with string/M-theory. We discover an OPE universality at the string scale: to leading order in large $N$, heavy-heavy-light three-point functions, with heavy operators that are parametrically lighter than a power of $N$, are linear in the heavy conformal dimension. We explore its consequences for supersymmetric CFTs and explain how emergent large extra dimensions relate to a Sublattice Weak Gravity Conjecture for CFTs. Lastly, we conjecture, building on a claim of arXiv:0908.0756, that any CFT with large higher-spin gap and no global symmetries has a holographic hierarchy: $D=d+1$
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