Fading Gravity and Self-Inflation

We study the cosmology of a toy modified theory of gravity in which gravity shuts off at short distances, as in the fat graviton scenario of Sundrum. In the weak-field limit, the theory is perturbatively local, ghost-free and unitary, although likely suffers from non-perturbative instabilities. We derive novel self-inflationary solutions from the vacuum equations of the theory, without invoking scalar fields or other forms of stress energy. The modified perturbation equation expressed in terms of the Newtonian potential closely resembles its counterpart for inflaton fluctuations. The resulting scalar spectrum is therefore slightly red, akin to the simplest scalar-driven inflationary models. A key difference, however, is that the gravitational wave spectrum is generically not scale invariant. In particular the tensor spectrum can have a blue tilt, a distinguishing feature from standard inflation.Comment: 35 pages, 4 figures. v3: version to appear in Phys. Rev.

Quantum Isometrodynamics

Classical Isometrodynamics is quantized in the Euclidean plus axial gauge. The quantization is then generalized to a broad class of gauges and the generating functional for the Green functions of Quantum Isometrodynamics (QID) is derived. Feynman rules in covariant Euclidean gauges are determined and QID is shown to be renormalizable by power counting. Asymptotic states are discussed and new quantum numbers related to the "inner" degrees of freedom introduced. The one-loop effective action in a Euclidean background gauge is formally calculated and shown to be finite and gauge-invariant after renormalization and a consistent definition of the arising "inner" space momentum integrals. Pure QID is shown to be asymptotically free for all dimensions of "inner" space $D$ whereas QID coupled to the Standard Model fields is not asymptotically free for D <= 7. Finally nilpotent BRST transformations for Isometrodynamics are derived along with the BRST symmetry of the theory and a scetch of the general proof of renormalizability for QID is given.Comment: 38 page

Effective Field Theory for the Quantum Electrodynamics of a Graphene Wire

We study the low-energy quantum electrodynamics of electrons and holes, in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/p_T, where p_T is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest-order in (p/p_T), our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound-states, and we calculate the dispersion law of such modes. We also compute the DC conductivity per unit length at zero chemical potential and find g_s =e^2/h, where g_s=4 is the degeneracy factor.Comment: 7 pages, 2 figures. Definitive version, accepted for publication on Phys. Rev.

Gauged supersymmetries in Yang-Mills theory

In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some non-renormalization theorems with practical simplifications for perturbation theory. We show in particular that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of non-zero Curci-Ferrari mass is also addressed.Comment: 11 pages. Minor changes. Some added reference

Breakdown of the perturbative renormalization group at certain quantum critical points

It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from finite-order perturbative renormalization-group treatments may be not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a non-renormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.Comment: 4pp, 1 eps fi

Symbol calculus and zeta--function regularized determinants

In this work, we use semigroup integral to evaluate zeta-function regularized determinants. This is especially powerful for non--positive operators such as the Dirac operator. In order to understand fully the quantum effective action one should know not only the potential term but also the leading kinetic term. In this purpose we use the Weyl type of symbol calculus to evaluate the determinant as a derivative expansion. The technique is applied both to a spin--0 bosonic operator and to the Dirac operator coupled to a scalar field.Comment: Added references, some typos corrected, published versio

The Effect of Interactions on the Conductance of Graphene Nanoribbons

We study the effects of the interaction between electrons and holes on the conductance G of quasi-one-dimensional graphene systems. We first consider as a benchmark the limit in which all interactions are negligible, recovering the predictions of the tight-binding approximation for the spectrum of the system, and the well-known result G=4 e^2/h for the lowest conductance quantum. Then we consider an exactly solvable field theoretical model in which the electro-magnetic interactions are effectively local. Finally, we use the effective field theory formalism to develop an exactly solvable model in which we also include the effect of non-local interactions. We find that such interactions turn the nominally metallic armchair graphene nanoribbon into a semi-conductor, while the short-range interactions lead to a correction to the G=4 e^2/h formula.Comment: 9 pages, 1 figur

Critical behavior of supersymmetric O(N) models in the large-N limit

We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric O(N) model in three dimensions. For a supersymmetric optimized regulator function we solve the RG equation for the superpotential exactly in the large-N limit. The fixed-point solutions are classified by an exactly marginal coupling. In the weakly coupled regime there exists a unique fixed point solution, for intermediate couplings we find two separate fixed point solutions and in the strong coupling regime no globally defined fixed-point potentials exist. We determine the exact critical exponents both for the superpotential and the associated scalar potential. Finally we relate the high-temperature limit of the four-dimensional theory to the Wilson-Fisher fixed point of the purely scalar theory.Comment: 13 pages,4 figure

A Class of Nonperturbative Configurations in Abelian-Higgs Models: Complexity from Dynamical Symmetry Breaking

We present a numerical investigation of the dynamics of symmetry breaking in both Abelian and non-Abelian $[S U (2)]$ Higgs models in three spatial dimensions. We find a class of time-dependent, long-lived nonperturbative field configurations within the range of parameters corresponding to type-1 superconductors, that is, with vector masses ($m_v$) larger than scalar masses ($m_s$). We argue that these emergent nontopological configurations are related to oscillons found previously in other contexts. For the Abelian-Higgs model, our lattice implementation allows us to map the range of parameter space -- the values of $\beta = (m_s /m_v)^2$ -- where such configurations exist and to follow them for times t \sim \O(10^5) m^{-1}. An investigation of their properties for $\hat z$-symmetric models reveals an enormously rich structure of resonances and mode-mode oscillations reminiscent of excited atomic states. For the SU(2) case, we present preliminary results indicating the presence of similar oscillonic configurations.Comment: 21 pages, 19 figures, prd, revte

Symmetry improvement of 3PI effective actions for O(N) scalar field theory

[Abridged] n-Particle Irreducible Effective Actions ($n$PIEA) are a powerful tool for extracting non-perturbative and non-equilibrium physics from quantum field theories. Unfortunately, practical truncations of $n$PIEA can unphysically violate symmetries. Pilaftsis and Teresi (PT) addressed this by introducing a "symmetry improvement" scheme in the context of the 2PIEA for an O(2) scalar theory, ensuring that the Goldstone boson is massless in the broken symmetry phase [A. Pilaftsis and D. Teresi, Nuc.Phys. B 874, 2 (2013), pp. 594--619]. We extend this by introducing a symmetry improved 3PIEA for O(N) theories, for which the basic variables are the 1-, 2- and 3-point correlation functions. This requires the imposition of a Ward identity involving the 3-point function. The method leads to an infinity of physically distinct schemes, though an analogue of d'Alembert's principle is used to single out a unique scheme. The standard equivalence hierarchy of $n$PIEA no longer holds with symmetry improvement and we investigate the difference between the symmetry improved 3PIEA and 2PIEA. We present renormalized equations of motion and counter-terms for 2 and 3 loop truncations of the effective action, leaving their numerical solution to future work. We solve the Hartree-Fock approximation and find that our method achieves a middle ground between the unimproved 2PIEA and PT methods. The phase transition predicted by our method is weakly first order and the Goldstone theorem is satisfied. We also show that, in contrast to PT, the symmetry improved 3PIEA at 2 loops does not predict the correct Higgs decay rate, but does at 3 loops. These results suggest that symmetry improvement should not be applied to $n$PIEA truncated to $<n$ loops. We also show that symmetry improvement is compatible with the Coleman-Mermin-Wagner theorem, a check on the consistency of the formalism.Comment: 27 pages, 15 figures, 2 supplemental Mathematica notebooks. REVTeX 4.1 with amsmath. Updated with minor corrections. Accepted for publication in Phys. Rev.