Properties of effective massive Yang-Mills theory in the limit of vanishing vector boson mass (original) (raw)

An effective action for Yang-Mills field strengths

Nuclear Physics B, 1990

We investigate the gauge-invariant semi-classical effective action for the field strength tensor of Yang-Mills theories and emphasize that renormalization introduces a physical scale in this formulation. The stationary points of the renormalized action are partially classified by a topological number, and imply a non-vanishing (G 2). For SU(2) all homogeneous vacuum solutions are explicitly constructed, for SU(3) numerical results are presented. The SU(2) and SU(3) ground states are found to differ qualitatively. An effective fermion theory is extracted which in the low-momentum regime reduces to a particular four-point interaction, but resembles gluon exchange at high momentum transfers.

One-loop renormalization of the Yang-Mills theory with BRST-invariant mass term

Divergent part of the one-loop effective action for the Yang-Mills theory in a special gauge containing forth degrees of ghost fields and allowing addition of BRST-invariant mass term is calculated by the generalized t'Hooft-Veltman technique. The result is BRST-invariant and defines running mass, coupling constant and parameter of the gauge.

The Effective Potential of the N = 0* Yang-Mills Theory

Journal of High Energy Physics, 2004

We study the N = 4 SYM theory with SU(N ) gauge group in the large N limit, deformed by giving equal mass to the four adjoint fermions. With this modification, a potential is dynamically generated for the six scalars in the theory, φ i . We show that the resulting theory is stable (perturbatively in the 't Hooft coupling), and that there are some indications that φ = 0 is the vacuum of the theory. Using the AdS/CFT correspondence, we compare the results to the corresponding supergravity computation, i.e. brane probing a deformed AdS 5 × S 5 background, and we find qualitative agreement.

QCD Theory of the Hadrons and Filling the Yang–Mills Mass Gap

Symmetry, 2020

The rank-3 antisymmetric tensors which are the magnetic monopoles of SU(N) Yang-Mills gauge theory dynamics, unlike their counterparts in Maxwell's U(1) electrodynamics, are non-vanishing, and do permit a net flux of Yang-Mills analogs to the magnetic field through closed spatial surfaces. When electric source currents of the same Yang-Mills dynamics are inverted and their fermions inserted into these Yang-Mills monopoles to create a system, this system in its unperturbed state contains exactly three fermions due to the monopole rank-3 and its three additive field strength gradient terms in covariant form. So to ensure that every fermion in this system occupies an exclusive quantum state, the Exclusion Principle is used to place each of the three fermions into the fundamental representation of the simple gauge group with an SU(3) symmetry. After the symmetry of the monopole is broken to make this system indivisible, the gauge bosons inside the monopole become massless, the SU(3) color symmetry of the fermions becomes exact, and a propagator is established for each fermion. The monopoles then have the same antisymmetric color singlet wavefunction as a baryon, and the field quanta of the magnetic fields fluxing through the monopole surface have the same symmetric color singlet wavefunction as a meson. Consequently, we are able to identify these fermions with colored quarks, the gauge bosons with gluons, the magnetic monopoles with baryons, and the fluxing entities with mesons, while establishing that the quarks and gluons remain confined and identifying the symmetry breaking with hadronization. Analytic tools developed along the way are then used to fill the Yang-Mills mass gap.

vs. pole masses of gauge bosons: electroweak bosonic two-loop corrections

Nuclear Physics B, 2002

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represent a gauge invariant subclass of diagrams. All calculations were performed in the linear R ξ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters sin 2 θ W and the mass ratio m 2 Z /m 2 H . We also present the corresponding on-shell mass counter-terms for the massive gauge bosons, which will be needed for the calculation of observables at two-loops in the on-shell renormalization scheme.

Generalization of the Yang–Mills theory

International Journal of Modern Physics A, 2016

We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincaré algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan–Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that ...

Mass generation in Yang-Mills theories

EPJ Web of Conferences, 2017

In this talk we review recent progress on our understanding of the nonperturbative phenomenon of mass generation in non-Abelian gauge theories, and the way it manifests itself at the level of the gluon propagator, thus establishing a close contact with a variety of results obtained in large-volume lattice simulations. The key observation is that, due to an exact cancellation operating at the level of the Schwinger-Dyson equations, the gluon propagator remains rigorously massless, provided that the fully-dressed vertices of the theory do not contain massless poles. The inclusion of such poles activates the well-known Schwinger mechanism, which permits the evasion of the aforementioned cancellation, and accounts for the observed infrared finiteness of the gluon propagator both in the Landau gauge and away from it.

On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories

Journal of High Energy Physics, 2002

We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU (2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling properties of physical objects-magnetic vortices, as first argued by Greensite et. al. We can show that a local gauge transformation of a certain type can "create" abelian monopole-antimonopole pairs along magnetic vortices. This gauge transformation exists in pure SU (N) gauge theory at any N .

One-loop effective potential in higher-dimensional Yang-Mills theory

Fortschritte Der Physik-progress of Physics, 1999

We study the effective action in Euclidean Yang-Mills theory with a compact simple gauge group in one-loop approximation assuming a covariantly constant gauge field strength as a background. For groups of higher rank and spacetimes of higher dimensions such field configurations have many independent color components taking values in Cartan subalgebra and many "magnetic fields" in each color component. In our previous investigation it was shown that such background is stable in dimensions higher than four provided the amplitudes of "magnetic fields" do not differ much from each other. In the present paper we exactly calculate the relevant zeta-functions in the case of equal amplitudes of "magnetic fields". For two "magnetic fields" with equal amplitudes the behavior of the effective action is studied in detail. It is shown that in dimensions d = 4, 5, 6, 7 (mod 8), the perturbative vacuum is metastable, i.e., it is stable in perturbation theory but the effective action is not bounded from below, whereas in dimensions d = 9, 10, 11 (mod 8) the perturbative vacuum is absolutely stable. In dimensions d = 8 (mod 8) the perturbative vacuum is stable for small values of the coupling constant but becomes unstable for large coupling constant leading to the formation of a non-perturbative stable vacuum with nonvanishing "magnetic fields". The critical value of the coupling constant and the amplitudes of the vacuum "magnetic fields" are evaluated exactly.