Massive Yang-Mills Theory Research Articles

The strong couplings of massive Yang-Mills theory

We study the massive Yang-Mills theory in which the mass term is added by hand. The standard perturbative approach suggests that the massless limit of this theory is not smooth. We confirm that this issue is related to the existence of additional degrees of freedom, which are absent in the massless theory. Nevertheless, we show that the longitudinal modes become strongly coupled at the Vainshtein scale, which coincides with the scale of the unitarity violation. Beyond this scale, they decouple from the remaining degrees of freedom, and the massless theory is restored up to small corrections. From here, it follows that the apparent discontinuity in the massless limit is only an artefact of the perturbation theory. The massless limit of massive Yang-Mills theory is smooth, as originally proposed in [21].

A Review of Third Way Consistent Theories

We will give an overview of “third way consistent” theories. Field equations of such models do not come from the variation of a local action without auxiliary fields, yet their covariant divergences still vanish on-shell. First examples were discovered in three dimensions which were pure massive gravity and Yang-Mills theories. However, recently interacting p-form theories with this property in arbitrary dimensions were also constructed. After explaining construction of these theories and some of their general features, we will discuss some open problems and future directions.

Novel 3D supersymmetric massive Yang-Mills theory

We construct three-dimensional, $\mathcal{N}=1$ off-shell supersymmetric massive Yang-Mills (YM) theory whose YM equation is ``third-way'' consistent. This means that the field equations of this model do not come from variation of a local action without additional fields, yet the gauge-covariant divergence of the YM equation still vanishes on shell. To achieve this, we modify the massive Majorana spinor equation so that its supersymmetry variation gives a modified YM equation whose bosonic part coincides with the third-way consistent pure massive YM model.

Gravitating Meron-like topological solitons in massive Yang\u2013Mills theory and the Einstein\u2013Skyrme model

We show that Merons in D-dimensional Einstein–Massive–Yang–Mills theory can be mapped to solutions of the Einstein–Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connection A=lambda U^{-1}dU, the massive Yang–Mills equations reduce to the Skyrme equations for the corresponding group element U. In the same way, the energy–momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the SU(2) case and show that introducing a mass for the Yang–Mills field restricts Merons to live on geometries given by the direct product of S^3 (or S^2) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for D=4 and D=5. Finally, we comment on possible generalisations.

Massive gravity from double copy

We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

Doubly charmed Ξcc molecular states from meson-baryon interaction

Stimulated by the new experimental LHCb findings associated with the $\Omega_c$ states, some of which we have described in a previous work as being dynamically generated through meson-baryon interaction, we have extended this approach to make predictions for new $\Xi_{cc}$ molecular states in the $C=2$, $S=0$ and $I=1/2$ sector. These states manifest themselves as poles in the solution of the Bethe-Salpeter equation in coupled channels. The kernels of this equation were obtained using the Lagrangians coming from the hidden local gauge symmetry, where the interactions are dominated by the exchange of light vector mesons. The extension of this approach to the heavy sector stems from the realization that the dominant interaction corresponds to having the heavy quarks as spectators, which implies the preservation of the heavy quark symmetry. As a result, we get several states: two states from the pseudoscalar meson-baryon interaction with $J^P=1/2^-$, and masses around $4080$ and $4090$ MeV, and one at $4150$ MeV for $J^P=3/2^-$. Furthermore, from the vector meson-baryon interaction we get three states degenerate with $J^P=1/2^-$ and $3/2^-$ from $4220$ MeV to $4330$ MeV, and two more states around $4280$ MeV and $4410$ MeV, degenerate with $J^P=1/2^-,\, 3/2^-$ and $5/2^-$.

Consistent deformations of free massive field theories in the Stueckelberg formulation

Cohomological techniques within the Batalin-Vilkovisky (BV) extension of the Becchi-Rouet-Stora-Tyutin (BRST) formalism have proved invaluable for classifying consistent deformations of gauge theories. In this work we investigate the application of this idea to massive field theories in the Stueckelberg formulation. Starting with a collection of free massive vectors, we show that the cohomological method reproduces the cubic and quartic vertices of massive Yang-Mills theory. In the same way, taking a Fierz-Pauli graviton on a maximally symmetric space as the starting point, we are able to recover the consistent cubic vertices of nonlinear massive gravity. The formalism further sheds light on the characterization of Stueckelberg gauge theories, by demonstrating for instance that the gauge algebra of such models is necessarily Abelian and that they admit a Born-Infeld-like formulation in which the action is simply a combination of the gauge-invariant structures of the free theory.

Polysymplectic formulation for topologically massive Yang–Mills field theory

We analyze the De Donder–Weyl covariant field equations for the topologically massive Yang–Mills theory. These equations are obtained through the Poisson–Gerstenhaber bracket described within the polysymplectic framework. Even though the Lagrangian defining the system of our interest is singular, we show that by appropriately choosing the polymomenta one may obtain an equivalent regular Lagrangian, thus avoiding the standard analysis of constraints. Further, our simple treatment allows us to only consider the privileged [Formula: see text]-forms in order to obtain the correct field equations, in opposition to certain examples found in the literature.

Gluon bound state and asymptotic freedom derived from the Bethe–Salpeter equation

In this paper we study the two-body bound states for gluons and ghosts in a massive Yang-Mills theory which is obtained by generalizing the ordinary massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we give a systematic derivation of the coupled Bethe-Salpeter equations for gluons and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the composite operators within the framework of the path integral quantization. Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude representing the simultaneous bound states of gluons and ghosts by solving the homogeneous Bethe-Salpeter equation in the ladder approximation. We study how the inclusion of ghosts affects the two-gluon bound states in the cases of the standing and running gauge coupling constant. Moreover, we show explicitly that the approximate solutions obtained for the gluon-gluon amplitude are consistent with the ultraviolet asymptotic freedom signaled by the negative $\beta$ function.

Gauge field spectrum in massive Yang-Mills theory with Lorentz violation

The spectrum of the massive CPT-odd Yang-Mills propagator with Lorentz violation is performed at tree-level. The modification is due to mass terms generated by the exigence of multiplicative renormalizability of Yang-Mills theory with Lorentz violation. The causality analysis is performed from group and front velocities for both, spacelike and timelike background tensors. It is show that, by demanding causality, it is always possible to define a physical sector for the gauge propagator. Hence, it is expected that the model is also unitary, if one takes the Faddeev-Popov ghost into account.

Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

We examine the phase structure of massive Yang-Mills theory in 1+1 dimensions. This theory is equivalent to a gauged principal chiral sigma model. It has been previously shown that the gauged theory has only a confined phase, and no Higgs phase in the continuum, and at infinite volume. There are no massive gluons, but only hadron-like bound states of sigma-model particles. The reason is that the gluon mass diverges, being proportional to the two-point correlation function of the renormalized field of the sigma model at $x=0$. We use exact large-$N$ results to show that after introducing a lattice regularization and typical values of the coupling constants used in Monte Carlo simulations, the gluon mass becomes finite, and even sometimes small. A smooth crossover into a Higgs phase can then appear. For small volumes and large $N$, we find an analytic expression for the gluon mass, which depends on the coupling constants and the volume. We argue that this Higgs phase is qualitatively similar to the one observed in lattice computations at $N=2$.

Topologically massive Yang–Mills theory and link invariants

Topologically massive Yang–Mills theory is studied in the framework of geometric quantization. Since this theory has a mass gap proportional to the topological mass m, Yang–Mills contribution decays exponentially at very large distances compared to 1/m, leaving a pure Chern–Simons theory with level number k. In this paper, the near Chern–Simons limit is studied where the distance is large enough to give an almost topological theory, with a small contribution from the Yang–Mills term. It is shown that this almost topological theory consists of two copies of Chern–Simons with level number k/2, very similar to the Chern–Simons splitting of topologically massive AdS gravity. Also, gauge invariance of these half-Chern–Simons theories is discussed. As m approaches to infinity, the split parts add up to give the original Chern–Simons term with level k. Reduction of the phase space is discussed in this limit. Finally, a relation between the observables of topologically massive Yang–Mills theory and Chern–Simons theory is shown. One of the two split Chern–Simons pieces is shown to be associated with Wilson loops while the other with 't Hooft loops. This allows one to use skein relations to calculate topologically massive Yang–Mills theory observables in the near Chern–Simons limit.

Properties of effective massive Yang-Mills theory in the limit of vanishing vector boson mass

Two-loop corrections to the pole mass of the vector boson and the pole masses and the magnetic moments of fermions are calculated in the framework of an effective field theory of massive Yang-Mills fields interacting with fermions. It is shown that the limit of vanishing vector boson mass is finite for all these quantities. Implications of the obtained results are discussed.

Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis

We analyse the constraint structure of the topologically massive Yang-Mills theory in instant-form and null-plane dynamics via the Hamilton-Jacobi formalism. The complete set of hamiltonians that generates the dynamics of the system is obtained from the Frobenius’ integrability conditions, as well as its characteristic equations. As generators of canonical transformations, the hamiltonians are naturally linked to the generator of Lagrangian gauge transformations.

On mass-shell renormalizability of the massive Yang-Mills theory

It is shown that the massive Yang-Mills theory is on mass-shell renormalizable. Thus the Standard Model of electroweak interactions can be modified by removing terms with the scalar field from the Lagrangian in the unitary gauge. The resulting electroweak theory without the Higgs particle is on mass-shell renormalizable and unitary.

Physical unitarity for a massive Yang-Mills theory without the Higgs field: A perturbative treatment

In a series of papers, we examine the physical unitarity in a massive Yang-Mills theory without the Higgs field in which the color gauge symmetry is not spontaneously broken and kept intact. For this purpose, we use a new framework proposed in the previous paper Kondo [arXiv:1208.3521] based on a nonperturbative construction of a non-Abelian field describing a massive spin-one vector boson field, which enables us to perform the perturbative and nonperturbative studies on the physical unitarity. In this paper, we present a new perturbative treatment for the physical unitarity after giving the general properties of the massive Yang-Mills theory. Then we reproduce the violation of physical unitarity in a transparent way. This paper is a preliminary work to the subsequent papers in which we present a nonperturbative framework to propose a possible scenario of restoring the physical unitarity in the Curci-Ferrari model.

Erratum: One-loop self-energy and counterterms in a massive Yang-Mills theory based on the nonlinearly realized gauge group [Phys. Rev. D77, 105012 (2008)

Erratum: One-loop self-energy and counterterms in a massive Yang-Mills theory based on the nonlinearly realized gauge group [Phys. Rev. D<b>77</b>, 105012 (2008)

Symmetry group of massive Yang–Mills theories without Higgs and their quantization

We analyze the symmetry group of massive Yang–Mills theories and their quantization strongly motivated by an already proposed alternative to the standard model of electroweak interactions without Higgs. In these models the mass generation of the intermediate vector bosons is based on a non-Abelian Stueckelberg mechanism, where the dynamics of the Goldstone-like bosons is addressed by a partial-trace nonlinear-sigma piece of the Lagrangian. In spite of the high nonlinearity of the scalar sector, the existence of an infinite number of symmetries, extending the traditional gauge group, allows us to sketch a group-theoretical quantization algorithm specially suited to nonlinear systems, which departs from usual canonical quantization. On the quantum representation space of this extended symmetry group, a quantum Hamiltonian preserving the representation can be given, whose classical analog reproduces the equations of motion.

MASS DEFORMATIONS OF SUPER YANG–MILLS THEORIES IN D = 2 + 1, AND SUPER-MEMBRANES: A NOTE

Mass deformations of supersymmetric Yang–Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a nonlocal gauge and Poincaré invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass-deformed gauge theories defined on R3 or R × T2 produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang–Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang–Mills theories in three spacetime dimensions. Explicit formulas for the gauge theory actions are provided.

One-loop self-energy and counterterms in a massive Yang-Mills theory based on the nonlinearly realized gauge group

In this paper we evaluate the self-energy of the vector mesons at one loop in our recently proposed subtraction scheme for massive nonlinearly realized SU(2) Yang-Mills theory. We check the fulfillment of physical unitarity. The resulting self-mass can be compared with the value obtained in the massive Yang-Mills theory based on the Higgs mechanism, consisting in extra terms due to the presence of the Higgs boson (tadpoles included). Moreover we evaluate all the one-loop counterterms necessary for the next order calculations. By construction they satisfy all the equations of the model (Slavnov-Taylor, local functional equation and Landau gauge equation). They are sufficient to make all the one-loop amplitudes finite through the hierarchy encoded in the local functional equation.