Is Barbero's Hamiltonian formulation a Gauge Theory of Lorentzian Gravity?

This letter is a critique of Barbero's constrained Hamiltonian formulation of General Relativity on which current work in Loop Quantum Gravity is based. While we do not dispute the correctness of Barbero's formulation of general relativity, we offer some criticisms of an aesthetic nature. We point out that unlike Ashtekar's complex SU(2) connection, Barbero's real SO(3) connection does not admit an interpretation as a space-time gauge field. We show that if one tries to interpret Barbero's real SO(3) connection as a space-time gauge field, the theory is not diffeomorphism invariant. We conclude that Barbero's formulation is not a gauge theory of gravity in the sense that Ashtekar's Hamiltonian formulation is. The advantages of Barbero's real connection formulation have been bought at the price of giving up the description of gravity as a gauge field.Comment: 12 pages, no figures, revised in the light of referee's comments, accepted for publication in Classical and Quantum Gravit

Chiral bosonization for non-commutative fields

A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to $(1+ \theta^2)$ where $\theta$ is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to $c^{\prime} = c \sqrt{1+\theta^2}$ where $c$ is the speed of light. Lorentz invariance remains intact if $c$ is rescaled by $c \to c^{\prime}$. The dispersion relation for bosons and fermions, in this case, is given by $\omega = c^{\prime} | k|$.Comment: 16 pages, JHEP style, version published in JHE

Charged Particles in a 2+1 Curved Background

The coupling to a 2+1 background geometry of a quantized charged test particle in a strong magnetic field is analyzed. Canonical operators adapting to the fast and slow freedoms produce a natural expansion in the inverse square root of the magnetic field strength. The fast freedom is solved to the second order. At any given time, space is parameterized by a couple of conjugate operators and effectively behaves as the `phase space' of the slow freedom. The slow Hamiltonian depends on the magnetic field norm, its covariant derivatives, the scalar curvature and presents a peculiar coupling with the spin-connection.Comment: 22 page

Quantum heat transfer through an atomic wire

We studied the phononic heat transfer through an atomic dielectric wire with both infinite and finite lengths by using a model Hamiltonian approach. At low temperature under ballistic transport, the thermal conductance contributed by each phonon branch of a uniform and harmonic chain cannot exceed the well-known value which depends linearly on temperature but is material independent. We predict that this ballistic thermal conductance will exhibit stepwise behavior as a function of temperature. By performing numerical calculations on a more realistic system, where a small atomic chain is placed between two reservoirs, we also found resonance modes, which should also lead to the stepwise behavior in the thermal conductance.Comment: 14 pages, 2 separate figure

Canonical Gravity, Diffeomorphisms and Objective Histories

This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the diffeomorphism invariance of the Lagrangian results in the following properties of the constrained Hamiltonian theory: the diffeomorphisms are generated by constraints on the phase space so that a) The algebra of the generators reflects the algebra of the diffeomorphism group. b) The Poisson brackets of the basic fields with the generators reflects the space-time transformation properties of these basic fields. This suggests that in a purely Hamiltonian approach the requirement of diffeomorphism invariance should be interpreted to include b) and not just a) as one might naively suppose. Giving up b) amounts to giving up objective histories, even at the classical level. This observation has implications for Loop Quantum Gravity which are spelled out in a companion paper. We also describe an analogy between canonical gravity and Relativistic particle dynamics to illustrate our main point.Comment: Latex 16 Pages, no figures, revised in the light of referees' comments, accepted for publication in Classical and Quantum Gravit

Realistic D-Brane Models on Warped Throats: Fluxes, Hierarchies and Moduli Stabilization

We describe the construction of string theory models with semirealistic spectrum in a sector of (anti) D3-branes located at an orbifold singularity at the bottom of a highly warped throat geometry, which is a generalisation of the Klebanov-Strassler deformed conifold. These models realise the Randall-Sundrum proposal to naturally generate the Planck/electroweak hierarchy in a concrete string theory embedding, and yielding interesting chiral open string spectra. We describe examples with Standard Model gauge group (or left-right symmetric extensions) and three families of SM fermions, with correct quantum numbers including hypercharge. The dilaton and complex structure moduli of the geometry are stabilised by the 3-form fluxes required to build the throat. We describe diverse issues concerning the stabilisation of geometric Kahler moduli, like blow-up modes of the orbifold singularities, via D term potentials and gauge theory non-perturbative effects, like gaugino condensation. This local geometry, once embedded in a full compactification, could give rise to models with all moduli stabilised, and with the potential to lead to de Sitter vacua. Issues of gauge unification, proton stability, supersymmetry breaking and Yukawa couplings are also discussed.Comment: 46 pages, 13 figures (figures 3 and 13 corrected

Uplifting and Inflation with D3 Branes

Back-reaction effects can modify the dynamics of mobile D3 branes moving within type IIB vacua, in a way which has recently become calculable. We identify some of the ways these effects can alter inflationary scenarios, with the following three results: (1) By examining how the forces on the brane due to moduli-stabilizing interactions modify the angular motion of D3 branes moving in Klebanov-Strassler type throats, we show how previous slow-roll analyses can remain unchanged for some brane trajectories, while being modified for other trajectories. These forces cause the D3 brane to sink to the bottom of the throat except in a narrow region close to the D7 brane, and do not ameliorate the \eta-problem of slow roll inflation in these throats; (2) We argue that a recently-proposed back-reaction on the dilaton field can be used to provide an alternative way of uplifting these compactifications to Minkowski or De Sitter vacua, without the need for a supersymmetry-breaking anti-D3 brane; and (3) by including also the D-term forces which arise when supersymmetry-breaking fluxes are included on D7 branes we identify the 4D supergravity interactions which capture the dynamics of D3 motion in D3/D7 inflationary scenarios. The form of these potentials sheds some light on recent discussions of how symmetries constrain D term interactions in the low-energy theory.Comment: JHEP.cls, 35 pages, 3 .eps figure

Racetrack Inflation

We develop a model of eternal topological inflation using a racetrack potential within the context of type IIB string theory with KKLT volume stabilization. The inflaton field is the imaginary part of the K\"ahler structure modulus, which is an axion-like field in the 4D effective field theory. This model does not require moving branes, and in this sense it is simpler than other models of string theory inflation. Contrary to single-exponential models, the structure of the potential in this example allows for the existence of saddle points between two degenerate local minima for which the slow-roll conditions can be satisfied in a particular range of parameter space. We conjecture that this type of inflation should be present in more general realizations of the modular landscape. We also consider `irrational' models having a dense set of minima, and discuss their possible relevance for the cosmological constant problem.Comment: 23 pages 7 figures. The final version with minor modifications, to appear in JHE

Inflation in Realistic D-Brane Models

We find successful models of D-brane/anti-brane inflation within a string context. We work within the GKP-KKLT class of type IIB string vacua for which many moduli are stabilized through fluxes, as recently modified to include `realistic' orbifold sectors containing standard-model type particles. We allow all moduli to roll when searching for inflationary solutions and find that inflation is not generic inasmuch as special choices must be made for the parameters describing the vacuum. But given these choices inflation can occur for a reasonably wide range of initial conditions for the brane and antibrane. We find that D-terms associated with the orbifold blowing-up modes play an important role in the inflationary dynamics. Since the models contain a standard-model-like sector after inflation, they open up the possibility of addressing reheating issues. We calculate predictions for the CMB temperature fluctuations and find that these can be consistent with observations, but are generically not deep within the scale-invariant regime and so can allow appreciable values for $dn_s/d\ln k$ as well as predicting a potentially observable gravity-wave signal. It is also possible to generate some admixture of isocurvature fluctuations.Comment: 39 pages, 21 figures; added references; identified parameters combining successful inflation with strong warping, as needed for consistency of the approximation

Inflating in a Better Racetrack

We present a new version of our racetrack inflation scenario which, unlike our original proposal, is based on an explicit compactification of type IIB string theory: the Calabi-Yau manifold P^4_[1,1,1,6,9]. The axion-dilaton and all complex structure moduli are stabilized by fluxes. The remaining 2 Kahler moduli are stabilized by a nonperturbative superpotential, which has been explicitly computed. For this model we identify situations for which a linear combination of the axionic parts of the two Kahler moduli acts as an inflaton. As in our previous scenario, inflation begins at a saddle point of the scalar potential and proceeds as an eternal topological inflation. For a certain range of inflationary parameters, we obtain the COBE-normalized spectrum of metric perturbations and an inflationary scale of M = 3 x 10^{14} GeV. We discuss possible changes of parameters of our model and argue that anthropic considerations favor those parameters that lead to a nearly flat spectrum of inflationary perturbations, which in our case is characterized by the spectral index n_s = 0.95.Comment: 20 pages, 7 figures. Brief discussion on the non-gaussianity of this model, one more figure of the field trajectories added as well as other minor changes to the tex