We refer to the ground state of a gravitating, charged ideal fluid of fermions held at a finite chemical potential as an 'electron star'. In a holographic setting, electron stars are candidate gravity duals for strongly interacting finite fermion density systems. We show how electron stars develop an emergent Lifshitz scaling at low energies. This IR scaling region is a consequence of the two way interaction between emergent quantum critical bosonic modes and the finite density of fermions. By integrating from the IR region to an asymptotically AdS 4 spacetime, we compute basic properties of the electron stars, including their electrical conductivity. We emphasize the challenge of connecting UV and IR physics in strongly interacting finite density systems.arXiv:1008.2828v2 [hep-th] 6 Jan 20111 The broader context A challenge facing contemporary condensed matter theory is the description of a 2+1 dimensional finite density of fermions interacting with a gapless collective bosonic excitation, such as a spin density wave or emergent gauge field. Such theories arise, for instance, when a Fermi liquid is tuned across a quantum phase transition. The low energy dynamics of the system of fermions interacting with the critical bosonic mode can be characterised as metallic quantum criticality. While in 3+1 dimensions one can proceed to integrate out the fermions and obtain a stable Gaussian theory for the boson [1], this approach does not give correct answers in 2+1 dimensions, see e.g. [2,3,4], as it ignores an infinite number of nonlocal marginal couplings in the effective theory for the boson. One should not integrate out the fermions in this case but rather flow to a scaling regime involving both the boson and fermion fields. The resulting low energy theory is strongly interacting, e.g. [4].One might have hoped to perform a (vector) large N analysis as a perturbative handle on the theory. It has recently been demonstrated [5,6,4] that the vector large N expansion breaks down for 2+1 dimensional metallic quantum critical systems. This occurs because a potential IR divergence at high loop order is cured by a self-energy of order 1/N , leading to extra factors of N in the numerator in certain Feynman graphs. Partially motivated by these difficulties, in this paper we will use the holographic correspondence [7,8,9, 10] to study a strongly interacting system of gapless bosons with a finite density of fermions. Before proceeding we should note that more traditional approaches to this problem have also been proposed [11,12,13] and that our framework does not appear to include ingredients that are likely crucial for applications to the original systems of interest, such as Fermi lines with cold regions as well as hot spots. We will, however, describe the emergence of a low energy scaling regime from the interaction of critical bosons with a finite density of fermions. The essential physics of this process was noted in [14].In the holographic correspondence a charge density is implemented by a bulk Maxwell field, dual...

We show that in F-theory GUTs, a natural explanation of flavor hierarchies in the quark and lepton sector requires a single point of E 8 enhancement in the internal geometry, from which all Yukawa couplings originate. The monodromy group acting on the seven-brane configuration plays a key role in this analysis. Moreover, the E 8 structure automatically leads to the existence of the additional fields and interactions needed for minimal gauge mediated supersymmetry breaking, and almost nothing else. Surprisingly, we find that in all but one Dirac neutrino scenario the messenger fields in the gauge mediated supersymmetry breaking sector transform as vector-like pairs in the 10 ⊕ 10 of SU (5). We also classify dark matter candidates available from this enhancement point, and rule out both annihilating and decaying dark matter scenarios as explanations for the recent experiments PAMELA, ATIC and FERMI. In F-theory GUT models, a 10 − 100 MeV mass gravitino remains as the prime candidate for dark matter, thus suggesting an astrophysical origin for recent experimental signals.

We apply a small magnetic field to strongly interacting matter with a gravity dual description as an electron star. These systems are both metallic and quantum critical at low energies. The resulting quantum oscillations are shown to be of the Kosevich-Lifshitz form characteristic of Fermi liquid theory. It is seen that only fermions at a single radius in the electron star contribute to the oscillations. We proceed to show that the Fermi surface area extracted from the quantum oscillations does not obey the simplest statement of the Luttinger theorem, that is, it is not universally proportional to the total charge density. It follows that our system is a non-Fermi liquid that nonetheless exhibits Kosevich-Lifshitz quantum oscillations. We explain how the Luttinger count is recovered via a field theoretic description involving a continuum of 'smeared' fermionic excitations.

In this paper we study the interplay between the recently proposed F-theory GUTs and cosmology. Despite the fact that the parameter range for F-theory GUT models is very narrow, we find that F-theory GUTs beautifully satisfy most cosmological constraints without any further restrictions. The viability of the scenario hinges on the interplay between various components of the axion supermultiplet, which in F-theory GUTs is also responsible for breaking supersymmetry. In these models, the gravitino is the LSP and develops a mass by eating the axino mode. The radial component of the axion supermultiplet known as the saxion typically begins to oscillate in the early Universe, eventually coming to dominate the energy density. Its decay reheats the Universe to a temperature of ~ 1 GeV, igniting BBN and diluting all thermal relics such as the gravitino by a factor of ~ 10^(-4) - 10^(-5) such that gravitinos contribute a sizable component of the dark matter. In certain cases, non-thermally produced relics such as the axion, or gravitinos generated from the decay of the saxion can also contribute to the abundance of dark matter. Remarkably enough, this cosmological scenario turns out to be independent of the initial reheating temperature of the Universe. This is due to the fact that the initial oscillation temperature of the saxion coincides with the freeze out temperature for gravitinos in F-theory GUTs. We also find that saxion dilution is compatible with generating the desired baryon asymmetry from standard leptogenesis. Finally, the gravitino mass range in F-theory GUTs is 10-100 MeV, which interestingly coincides with the window of values required for the decay of the NLSP to solve the problem of Li(7) over-production.Comment: v3: 90 pages, 5 figures, improved figures and discussion of saxion mas

We study the formation of marginally trapped surfaces in the head-on collision of two shock waves both in anti-de Sitter and Minkowski space-time in various dimensions as a function of the spread of the energy density in transverse space. For D = 4 and D = 5 it is shown that there exists a critical value of this spread above which no solution to the trapped surface equation is found. In four dimensions the trapped surface at criticality has a finite size, whereas in five the critical size vanishes. In both cases we find scaling relations characterized by critical exponents. Finally, when D > 5 there is always a solution to the trapped surface equation for any transverse spread.