International Journal of Modern Physics A

This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror–fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the paper is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg–Wilson fermions. We end by pointing out possible directions for future studies.

We consider a scalar field theory in AdS_d+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ_- and Δ₊, respectively, where Δ_± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS₃/CFT₂ prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.

Within the context of a string-theory dual to gauge theories with gauge group SU(N_c) and large N_c, we identify a class of solutions to the background equations for which a suitably defined dual of the gauge coupling exhibits the features of a walking theory. We find evidence for three distinct, dynamically generated scales, characterizing walking, symmetry breaking and confinement, and we put them in correspondence with field theory by an analysis of the operators driving the flow.

A new Lorentz gauge gravity model with R²-type Lagrangian is proposed. In the absence of classical torsion, the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space–time background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin-2 mode of torsion becomes dynamical essentially due to the nonlinear structure of the theory. We perform covariant one-loop quantization of the model for a special case of constant curvature space–time background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced due to quantum dynamics of torsion.

We calculate the total energy of an exact spherically symmetric solutions, i.e. Schwarzschild and Reissner–Nordström, using the gravitational energy–momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical. Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.

The asymptotics of the SU(2) 15j-symbol are obtained using coherent states for the boundary data. The geometry of all nonsuppressed boundary data is given. For some boundary data, the resulting formula is interpreted in terms of the Regge action of the geometry of a 4-simplex in four-dimensional Euclidean space. This asymptotic formula can be used to derive and extend the asymptotics of the spin foam amplitudes for quantum gravity models. The relation of the SU(2) Ooguri model to these quantum gravity models and their continuum Lagrangians is discussed.

We analyze the active-galaxy correlation reported in 2007 by the Pierre Auger Collaboration. The signal diminishes if the correlation-function approach (counting all "source–event" pairs and not only "nearest neighbors") is used, suggesting that the correlation may reveal individual sources and not their population. We analyze available data on physical conditions in these individual correlated sources and conclude that acceleration of protons to the observed energies is hardly possible in any of these galaxies, while heavier nuclei would be deflected by the Galactic magnetic field thus spoiling the correlation. Our results question the Auger interpretation of the reported anisotropy signal but do not contradict to its explanation with intermediate-mass nuclei accelerated in Cen A.