Dimensional non-Abelian Gauge Theory Research Articles

Cold-atom quantum simulator for string and hadron dynamics in non-Abelian lattice gauge theory

We propose an analog quantum simulator for simulating real-time dynamics of $(1+1)$-dimensional non-Abelian gauge theory well within the existing capacity of ultracold-atom experiments. The scheme calls for the realization of a two-state ultracold fermionic system in a one-dimensional bipartite lattice, and the observation of subsequent tunneling dynamics. Being based on the loop string hadron formalism of $SU(2)$ lattice gauge theory, this simulation technique is completely $SU(2)$ invariant and simulates accurate dynamics of physical phenomena such as string breaking and/or pair production. The scheme is scalable and particularly effective in simulating the theory in the weak-coupling regime, and also a bulk limit of the theory in the strong-coupling regime up to certain approximations. This paper also presents a numerical benchmark comparison of the exact spectrum and real-time dynamics of lattice gauge theory to that of the atomic Hamiltonian with an experimentally realizable range of parameters.

Asymptotic symmetries in (d + 2)-dimensional gauge theories

We show that the subleading soft photon theorem in a (d + 2)-dimensional massless abelian gauge theory gives rise to a Ward identity corresponding to divergent large gauge transformations acting on the celestial sphere at null infinity. We further generalize our analysis to (d + 2)-dimensional non-abelian gauge theories and show that the leading and subleading soft gluon theorem give rise to Ward identities corresponding to asymptotic symmetries of the theory.

An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with ϑ-term

A toy model is proposed for four dimensional non-abelian gauge theories coupled to a large number of fermionic degrees of freedom. As the number of flavors is varied the gauge theory may be confining, walking or conformal. The toy model mimicking this feature is the two dimensional O(3) sigma model with a theta-term. For all theta the model is asymptotically free. For small theta the model is confining in the infra red, for theta = pi the model has a non-trivial infra red fixed point and consequently for theta slightly below pi the coupling walks. The first step in investigating the notoriously difficult systematic effects of the gauge theory in the toy model is to establish non-perturbatively that the theta parameter is actually a relevant coupling. This is done by showing that there exist quantities that are entirely given by the total topological charge and are well defined in the continuum limit and are non-zero, despite the fact that the topological susceptibility is divergent. More precisely it is established that the differences of connected correlation functions of the topological charge (the cumulants) are finite and non-zero and consequently there is only a single divergent parameter in Z(theta) but otherwise it is finite. This divergent constant can be removed by an appropriate counter term rendering the theory completely finite even at theta > 0.

Non-Abelian topological mass generation in four dimensions

We study the topological mass generation in the 4 dimensional non-Abelian gauge theory, which is the extension of Allen et al.’s work in the Abelian theory. It is crucial to introduce a one form auxiliary field in constructing the gauge invariant non-Abelian action which contains both the one form vector gauge field A and the two form antisymmetric tensor field B. As in the Abelian case, the topological coupling mB∧F, where F is the field strength of A, makes the transmutation among A and B possible, and consequently we see that the gauge field becomes massive. We find the BRST/anti-BRST transformation rule using the horizontality condition, and construct a BRST/anti-BRST invariant quantum action.

Vacuum Nodes in QCD atθ=π: Exact Results

We show that the vacuum functional of 3+1 dimensional non-abelian gauge theories vanishes for some classical field configurations $\psi_0(A)=0$ when the coefficient of the CP violating $\theta$--term becomes $\theta=\pi$ (mod. $2\pi$). Some of these classical configurations are explicitly identified and include sphalerons. The results shed new light into the non-perturbative behavior of non-abelian gauge theories and suggest a relevant role for these classical configurations in the confinement mechanism at $\theta=0$.

Note on regularization dependence of loop corrections to the non-Abelian Chern-Simons term.

Using dimensional regularization, we reobtain the result that no Chern-Simons term is induced radiatively at two-loop order in the (2+1)-dimensional non-Abelian gauge theory with massive fermions. We also confirm that the result is gauge invariant.

Field strength method and Gribov ambiguity in two dimensional non-Abelian gauge theory

Field strength method and Gribov ambiguity in two dimensional non-Abelian gauge theory

Instanton effects in bound-state dynamics

A systematic method is developed for computing the effects of instanton configurations on binding energies of threshold bound states. Weak coupling and the relevance of the dilute-gas approximation are assumed. The bound-state mass is extracted by studying the asymptotic behavior of the Euclidean two-point function of a current with the quantum numbers of the bound state in question. The formalism is illustrated both for the binding of scalar particles in a (1 + 1)-dimensional Higgs-Abelian model and for quark-antiquark binding in a (3 + 1)-dimensional non-Abelian gauge theory. In the latter case, interactions of exchanged quantum gluons with the background instanton fields are found to induce binding-energy shifts of the same order in the coupling $\ensuremath{\alpha}$ as direct interaction of quarks with the background fields. The static limit of the leading kernel arising from gluon-instanton interactions is found to depend linearly on the quark-antiquark separation.

On the phase transition towards permanent quark confinement

In quantized gauge field theories one can introduce sets of operators that modify the gauge-topological structure of the fields but whose physical effect is essentially local. In 2 + 1 dimensional non-Abelian gauge theories these operators form scalar fields and it is argued that when the local gauge symmetry is not spontaneously broken then these topological fields develop a vacuum expectation value and their mutual symmetry breaks spontaneously. It is shown that quarks are then permanently confined. In 3 + 1 dimensional non-Abelian gauge theories one finds that the topological operators and the gauge field operators form a closed algebra from which it is deduced that this system can be in one of the four different phases: (i) spontaneous breakdown via an explicit or composite Higgs field, (ii) no Higgs field but permanent confinement of gauge quantum numbers, (iii) Higgs effect and still confinement, presumably only if there is an unbroken subgroup, and (iv) an intermediate phase (critical point?) with massless particles. Finally, the algebra can be realized in a simple model where phases (i) and (ii) can be obtained from each other by dual transformation.

Quark confinement and topology of gauge theories

The phenomenon of quark confinement is known to be connected with the restoration of apparently broken gauge symmetry. In this paper we focus on a special mechanism which is responsible for such restoration. The major suggestion is that in the treatment of infrared problems certain classical field trajectories are of paramount importance, which trajectories connect seemingly degenerate vacua thereby eliminating the degeneracy. Initially, we demonstrate this mechanism in certain simple non-gauge models. In order of increasing difficulty, we next examine compact quantum electro-dynamics in 2 + 1 space-time dimensions- essentially a variant of unified models of the Georgi-Glashow type. In this case we prove that charge is confined and show that the force between two charges is independent of the distance between them. For small values of the fine structure constant this force is explicitly evaluated. Finally, we turn to the more realistic case of a 3 + 1 dimensional non-Abelian gauge theory, and analyse the contribution of a single pseudoparticle to the correlation functions. It is proposed that the quantum fluctuations of the pseudoparticle are inessential, and that the one-loop approximation is effectively correct even for the large scale pseudoparticles. The emergent conclusion then is that the renormalized Yang-Mills theory is reduced to the problem of evaluating the effects of those configurations which involve many pseudoparticles, due account being taken of the interactions between them. Some aspects of this last problem are also discussed.