Zero-coupling Limit Research Articles

Light ray fluctuation and lattice refinement of simplicial quantum gravity

In several approaches of non-perturbative quantum gravity, a major outstanding problem is to obtain results valid at the infinite lattice refinement limit. Working with Lorentzian simplicial quantum gravity, we compute light ray fluctuation probabilities in 3D and 4D across different lattices. In a simplified refined box model with the Einstein–Hilbert action, numerical results show that lattice refinement does not simply suppress or simply enhance light ray fluctuations, but actually drives very wide and very narrow light probability distributions towards intermediate ones. A comparison across lattices and across couplings reveals numerical hints at a lattice refinement fixed point associated with a universality class of couplings. The results fit the intuition that quantum spacetime fluctuations reflected by light ray fluctuations start wild microscopically and become mild macroscopically. The refined box model is limited by the assumption of a rigid frame at all scales. The present results suggest further studies around the zero-coupling limit to relax the simplifying assumptions of the model.

Universal physics of the few-body system of two neutrons and one flavored meson

We investigate the $s$-wave three-body system of two neutrons and one flavored meson with total spin-isospin $J=0,I=3/2$. The meson-neutron scattering length can become infinitely large in an unphysical region of the quark mass when extrapolated from strangeness to charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is manifest in the three-body system when the meson-neutron scattering length is extrapolated to the unitary limit of the two-body interaction. We thereby discuss the consequence of universal physics in the physical $K^{-}nn$ and $D^{0}nn$ systems.

On the pole content of coupled channels chiral approaches used for the [formula omitted] system

Several theoretical groups describe the antikaon–nucleon interaction at low energies within approaches based on the chiral SU(3) dynamics and including next-to-leading order contributions. We present a comparative analysis of the pertinent models and discuss in detail their pole contents. It is demonstrated that the approaches lead to very different predictions for the K−p amplitude extrapolated to subthreshold energies as well as for the K−n amplitude. The origin of the poles generated by the models is traced to the so-called zero coupling limit, in which the inter-channel couplings are switched off. This provides new insights into the pole contents of the various approaches. In particular, different concepts of forming the Λ(1405) resonance are revealed and constraints related to the appearance of such poles in a given approach are discussed.

S-matrix algebra of theAdS2×S2superstring

In this paper we find the Yangian algebra responsible for the integrability of the AdS2 X S2 X T^6 superstring in the planar limit. We demonstrate the symmetry of the corresponding exact S-matrix in the massive sector, including the presence of the secret symmetry. We give two alternative presentations of the Hopf algebra, along with related discussions on the issue of evaluation representations. We study the classical r-matrix, and re-discover the need for a secret symmetry also in this context. Finally, taking the simplifying zero-coupling limit of the S-matrix as a generating R-matrix for the Algebraic Bethe Ansatz, we obtain an effective model of free fermions on a periodic spin-chain. This limit should provide hints to the one-loop anomalous dimension of the mysterious superconformal quantum mechanics dual to the superstring theory in this geometry.

Self-dual non-Abelian vector multiplet in three dimensions

We present an $N=1$ supersymmetric non-Abelian compensator formulation for a vector multiplet in three dimensions. Our total field content is the off-shell vector multiplet $(A_{\ensuremath{\mu}}{}^{I},{\ensuremath{\lambda}}^{I})$ with the off-shell scalar multiplet $({\ensuremath{\varphi}}^{I},{\ensuremath{\chi}}^{I};{F}^{I})$ both in the adjoint representation of an arbitrary non-Abelian gauge group. This system is reduced to a supersymmetric $\ensuremath{\sigma}$ model on a group manifold, in the zero-coupling limit. Based on this result, we formulate a `self-dual' non-Abelian vector multiplet in three dimensions. By an appropriate identification of parameters, the mass of the self-dual vector multiplet is quantized. Additionally, we also show that the self-dual non-Abelian vector multiplet can be coupled to the supersymmetric Dirac-Born-Infeld action. These results are further reformulated in superspace to get a clear overall picture.

Quantization of a nonlocal Abelian gauge theory and certain local-limit implications.

We formulate a path integral for quantizing a nonlocal Abelian gauge theory without matter fields. Having specified the precise meaning of local limit we perform a strong-coupling calculation in the continuum which leads to the confinement property, in this limit. Finally, it is also shown that the zero-coupling limit of the theory yields Maxwell's theory in its quantized form.

Dilation operator in gauge theories

The electromagnetic field is expanded in a series of O(4) eigenstates of total spin, and quantized by specifying commutators on surfaces of constant ${x}_{\ensuremath{\mu}}{x}^{\ensuremath{\mu}}={R}^{2}$ in four-dimensional Euclidean space. It is demonstrated that, under an arbitrary gauge transformation, some of the O(4) eigenstates are invariant; these gauge-invariant states are labeled by SU(2) \ensuremath{\bigotimes} SU(2) total (orbital plus internal) spin quantum numbers ($A$,$B$) and with $A\ensuremath{\ne}B$. Only these gauge-invariant states are nontrivial in the absence of sources, and are quantized. The leading-twist quantum states of the dilation field theory contain the minimum number of these dilation photons. The remaining spin degrees of freedom of the electromagnetic field are most simply written as a function of the form ${\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\varphi}(x)+{x}_{\ensuremath{\mu}}\frac{\ensuremath{\psi}(x)}{{R}^{2}}$. $\ensuremath{\varphi}(x)$ is obviously devoid of physics while $\ensuremath{\psi}(x)$ is a classical field propagating between radial projections of two electrical currents ${x}_{\ensuremath{\mu}}{J}^{\ensuremath{\mu}}(x)$ and ${y}_{\ensuremath{\mu}}{J}^{\ensuremath{\mu}}(y)$ only if ${x}_{\ensuremath{\mu}}{x}^{\ensuremath{\mu}}={y}_{\ensuremath{\mu}}{y}^{\ensuremath{\mu}}$. The quantization procedure described herein may be applied to non-Abelian theories. The procedure does not lead to a gauge-invariant decomposition of a non-Abelian field, but the identification of leading-twist quantum states is preserved in the zero-coupling limit.

Molecular Dynamics of Weakly Coupled Electric Dipoles on a Rigid Lattice. II. The Dielectric Response Function

The dielectric response function of a finite two-dimensional system of dipoles is evaluated numerically by the method of molecular dynamics. The dipoles are located on the sites of a rigid square lattice and are only allowed to rotate; the specimen itself is circular and includes 101, 193, or 421 dipoles. Two types of coupling are considered: (a) dipolar interactions and (b) classical exchange interactions favoring either parallel or antiparallel alignment. The corresponding response functions are largely different in each case. For dipolar interactions they differ rather little from the response function corresponding to zero coupling and the influence of the long-range part of the potential seems negligible. On the contrary, exchange interactions lead to response functions which deviate strongly from the zero-coupling limit, even when the coupling is rather weak. The Fourier transforms of these response functions and the corresponding Cole–Cole diagrams are constructed and discussed as well.

Grand-daughter trajectory in the ladder approximation

The ladder approximation in perturbation theory is used with scalar particles to evaluate those Regge trajectories that go tol=−1, −2 and −3 in the zero-coupling limit. Previous results concerning those that go to −2 are confirmed, that is that there is a daughter and two “sisters” of the daughter. It is shown that there is a grand-daughter going tol=−3 and a daughter for each of the sisters, together with two further trajectories. A check is made on the coefficients of the nonleading terms in the asymptotic behaviour, to verify that the contributions from parent and daughter are of the correct Regge character.