Initial Conditions for Critical Higgs Inflation

It has been pointed out that a large non-minimal coupling $\xi$ between the Higgs and the Ricci scalar can source higher derivative operators, which may change the predictions of Higgs inflation. A variant, called critical Higgs inflation, employs the near-criticality of the top mass to introduce an inflection point in the potential and lower drastically the value of $\xi$. We here study whether critical Higgs inflation can occur even if the pre-inflationary initial conditions do not satisfy the slow-roll behaviour (retaining translation and rotation symmetries). A positive answer is found: inflation turns out to be an attractor and therefore no fine-tuning of the initial conditions is necessary. A very large initial Higgs time-derivative (as compared to the potential energy density) is compensated by a moderate increase in the initial field value. These conclusions are reached by solving the exact Higgs equation without using the slow-roll approximation. This also allows us to treat consistently the inflection point, where the standard slow-roll approximation breaks down. Here we make use of an approach that is independent of the UV completion of gravity, by taking initial conditions that always involve sub-planckian energies.Comment: 8 pages, 5 figures; v2: comments and references added, version accepted for publication in Physics Letters

A Simple Motivated Completion of the Standard Model below the Planck Scale: Axions and Right-Handed Neutrinos

We study a simple Standard Model (SM) extension, which includes three families of right-handed neutrinos with generic non-trivial flavor structure and an economic implementation of the invisible axion idea. We find that in some regions of the parameter space this model accounts for all experimentally confirmed pieces of evidence for physics beyond the SM: it explains neutrino masses (via the type-I see-saw mechanism), dark matter, baryon asymmetry (through leptogenesis), solve the strong CP problem and has a stable electroweak vacuum. The last property may allow us to identify the Higgs field with the inflaton.Comment: 8 pages, 4 figures. Phys. Lett. B version: references and discussion on light right-handed neutrinos adde

Critical Higgs inflation in a Viable Motivated Model

An extension of the Standard Model with three right-handed neutrinos and a simple invisible axion model can account for all experimentally confirmed signals of new physics (neutrino oscillations, dark matter and baryon asymmetry) in addition to solving the strong CP problem, stabilizing the electroweak vacuum and satisfying all current observational bounds. We show that this model can also implement critical Higgs inflation, which corresponds to the frontier between stability and metastability of the electroweak vacuum. This leads to a value of the non-minimal coupling between the Higgs and the Ricci scalar that is much lower than the one usually quoted in Higgs inflation away from criticality. Then, an advantage is that the scale of perturbative unitarity breaking on flat spacetime can be very close to the Planck mass, where anyhow new physics is required. The higher dimensional operators are under control in this inflationary setup. The dependence of the cutoff on the Higgs background is also taken into account as appropriate when the Higgs is identified with the inflaton. Furthermore, critical Higgs inflation enjoys a robust inflationary attractor that makes it an appealing setup for the early universe. In the proposed model, unlike in the Standard Model, critical Higgs inflation can be realized without any tension with the observed quantities, such as the top mass and the strong coupling.Comment: 13 pages, 6 figures; v2: explanations and references added; v3: title changed and more explanations added (version accepted by PRD

Transitions in Dilaton Holography with Global or Local Symmetries

We study various transitions in dilaton holography, including those associated with the spontaneous breaking of a global (superfluid case) or local (superconductor case) U(1) symmetry in diverse dimensions d. By analyzing the thermodynamics of the dilaton-gravity system we find that scale invariance is broken at low temperatures, as shown by a nontrivial hyperscaling violation exponent in the infrared; increasing the temperature we recover scale symmetry in a d dependent way: while for d=2+1 a phase transition is found, for d=3+1 the transition is rather a crossover. This is the expected behavior of QCD where the number of colors N_c equals three (although in our holographic calculations N_c goes to infinity). When the U(1) is preserved and at low temperatures, the system is insulating for arbitrary d if the dilaton is appropriately coupled to the gauge field; for other couplings we also find a linear in temperature resistivity. We then determine the prediction of these models for several quantities in the superconducting phase: the DC and AC conductivity, the gap for charged excitations, the superfluid density, the vortex profiles, the coherence length, the penetration depth and the critical magnetic fields. We show that at low temperatures some of these quantities differ qualitatively compared with the corresponding models without the dilaton, although the superconductor is robustly of Type II. The ratio of the gap over the critical temperature of the superconductor is studied in detail varying d and the couplings of the dilaton and then compared with the BCS value. A holographic renormalization is required in d>2+1 to compute some quantities (such as the AC conductivity and the penetration depth) and we explain in detail how to perform it.Comment: 21 pages + references, 27 figures; v2: few comments and references added, matches the article published in JHE

Bulk Renormalization and Particle Spectrum in Codimension-Two Brane Worlds

We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).Comment: 18 pages, partly based on a talk given at IARD 2012: the eighth biennial conference on classical and quantum relativistic dynamics of particles and fields; v2: version published in Journal of Physics: Conference Serie

Superconductivity, Superfluidity and Holography

This is a concise review of holographic superconductors and superfluids. We highlight some predictions of the holographic models and the emphasis is given to physical aspects rather than to the technical details, although some references to understand the latter are systematically provided. We include gapped systems in the discussion, motivated by the physics of high-temperature superconductivity. In order to do so we consider a compactified extra dimension (with radius R), or, alternatively, a dilatonic field. The first setup can also be used to model cylindrical superconductors; when these are probed by an axial magnetic field a universal property of holography emerges: while for large R (compared to the other scales in the problem) non-local operators are suppressed, leading to the so called Little-Parks periodicity, the opposite limit shows non-local effects, e.g. the uplifting of the Little-Parks periodicity. This difference corresponds in the gravity side to a Hawking-Page phase transition.Comment: 10 pages, partly based on a talk given at DICE2012 (Spacetime - Matter - Quantum Mechanics from the Planck scale to emergent phenomena) and on a seminar given at the Gran Sasso National Laboratory; v2 references adde

Higgs Inflation at NNLO after the Boson Discovery

We obtain the bound on the Higgs and top masses to have Higgs inflation (where the Higgs field is non-minimally coupled to gravity) at full next-to-next-to-leading order (NNLO). Comparing the result obtained with the experimental values of the relevant parameters we find some tension, which we quantify. Higgs inflation, however, is not excluded at the moment as the measured values of the Higgs and top masses are close enough to the bound once experimental and theoretical uncertainties are taken into account.Comment: 7 pages, 3 figures; v2: few comments added to emphasize the importance of the results, published in Phys. Lett.

Quadratic Gravity

Adding terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory (QFT). The price to pay is a massive ghost, which is due to the higher derivatives that the terms quadratic in the curvature imply. In this paper the quadratic gravity scenario is reviewed including recent progress on the related stability problem of higher derivative theories. The renormalization of the theory is also reviewed and the final form of the full renormalization group equations in the presence of a generic renormalizable QFT is presented. The theory can be extrapolated up to infinite energy through the renormalization group if all matter couplings flow to a fixed point (either trivial or interacting). Moreover, besides reviewing the above-mentioned topics some further insight on the ghost issue and the infinite energy extrapolation is provided. There is the hope that in the future this scenario might provide a phenomenologically viable and UV complete relativistic field theory of all interactions.Comment: 46 pages, 4 figures, 2 tables. Review article prepared for Frontiers; v2 matches version published in Frontier

4D Effective Theory and Geometrical Approach

We consider the 4D effective theory for the light Kaluza-Klein (KK) modes. The heavy KK mode contribution is generally needed to reproduce the correct physical predictions: an equivalence, between the effective theory and the D-dimensional (or geometrical) approach to spontaneous symmetry breaking (SSB), emerges only if the heavy mode contribution is taken into account. This happens even if the heavy mode masses are at the Planck scale. In particular, we analyze a 6D Einstein-Maxwell model coupled to a charged scalar and fermions. Moreover, we briefly review non-Abelian and supersymmetric extensions of this theory.Comment: 7 pages, 2 figures. Proceeding for the Cairo International Conference on High Energy Physics (CICHEP II), 14 - 17 January 200

Chiral Asymmetry from a 5D Higgs Mechanism

An intriguing feature of the Standard Model is that the representations of the unbroken gauge symmetries are vector-like whereas those of the spontaneously broken gauge symmetries are chiral. Here we provide a toy model which shows that a natural explanation of this property could emerge in higher dimensional field theories and discuss the difficulties that arise in the attempt to construct a realistic theory. An interesting aspect of this type of models is that the 4D low energy effective theory is not generically gauge invariant. However, the non-invariant contributions to the observable quantities are very small, of the order of the square of the ratio between the light particle mass scale and the Kaluza-Klein mass scale. Remarkably, when we take the unbroken limit both the chiral asymmetry and the non-invariant terms disappear.Comment: 30 pages, 5 figures, uses axodraw.sty. Extended version, matches the article published on JHE