International Journal of Modern Physics A

We give an overview of the issue of anomalies in field theories with extra dimensions. We start by reviewing in a pedagogical way the computation of the standard perturbative gauge and gravitational anomalies on noncompact spaces, using Fujikawa's approach and functional integral methods, and discuss the available mechanisms for their cancellation. We then generalize these analyses to the case of orbifold field theories with compact internal dimensions, emphasizing the new aspects related to the presence of orbifold singularities and discrete Wilson lines, and the new cancellation mechanisms that are becoming available. We conclude with a very brief discussion on global and parity anomalies.

Considering the strong coupling to a field of two particles bound by a quark–quark-like potential, we calculate the energy and width of a hybrid state in a simplified model.

A generic F-theory compactification containing many D3 branes develops multiple brane throats. The interaction of observers residing inside different throats involves tunneling suppression and as a result, is very weak. This suggests a new mechanism for generating small numbers in Nature. One application is to the hierarchy problem: large supersymmetry breaking near the unification scale inside a shallow throat causes TeV-scale SUSY-breaking inside the standard-model throat. Another application, inspired by nuclear-decay, is in designing naturally long-lived particles: a cold dark matter particle residing near the standard model brane decays to an approximate CFT-state of a longer throat within a Hubble time. This suggests that most of the mass of the universe today could consist of CFT-matter and may soften structure formation at sub-galactic scales. The tunneling calculation demonstrates that the coupling between two throats is dominated by higher dimensional modes and consequently is much larger than a naive application of holography might suggest.

The possible anomaly of the tensor current divergence equation in U(1) gauge theories is calculated by means of perturbative method. It is found that the tensor current divergence equation is free of anomalies.

The nonlinear sigma model with a two-dimensional basis space and an n-dimensional target space is considered. Two different basis spaces are considered; the first is an 0(2)×0(2) subspace of the 0(2,2) projective space related to the Minkowski basis space, and the other is a toroidal space embedded into three-dimensional Euclidean space, characterized by radii R and r. The target space is taken to be an arbitrarily curved Riemannian manifold. One-loop dependence on the renormalization induced scale μ is shown in the toroidal basis space to be the same as in a flat or spherical basis space.

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T(2) of Wigner's little group for the free one-form Abelian gauge theory in four (3+1)-dimensions (4D) of space–time. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T(2) subgroup of the little group is quite well known, such a connection between the dual-gauge transformation and the little group is a new observation. The above connections are further elaborated and demonstrated in the framework of Becchi–Rouet–Stora–Tyutin (BRST) cohomology defined in the quantum Hilbert space of states where the Hodge decomposition theorem (HDT) plays a very decisive role.

We show how, modulo the distinction between the antipode and the "twisted" or "renormalized" antipode, Connes and Kreimer's algebraic paradigm trivializes the proofs of equivalence of the (corrected) Dyson–Salam, Bogoliubov–Parasiuk–Hepp and Zimmermann procedures for renormalizing Feynman amplitudes. We discuss the outlook for a parallel simplification of computations in quantum field theory, stemming from the same algebraic approach.

We study different Penrose limits of supergravity solution of NS5-brane in the presence of RR field. Although in the case of NS5-brane we get a four-dimensional plane wave, in the case with RR field we will get two different plane waves; a four-dimensional and a three-dimensional one. These plane wave solutions are the backgrounds that a particular string solution feels at one-loop approximation. Using the one-loop correction one can identify a particular subsector of LST/deformed LST which is dual to type II string theories on these plane waves.