On the Spectrum of Lattice Massive SU(2) Yang-Mills

On the basis of extended simulations we provide some results concerning the spectrum of Massive SU(2) Yang-Mills on the lattice. We study the "time" correlator of local gauge invariant operators integrated over the remaining three dimensions. The energy gaps are measured in the isospin I=0,1 and internal spin J=0,1 channels. No correlation is found in the I=1,J=0 channel. In the I=1, J=1 channel and far from the critical mass value $m_c$ the energy gap roughly follows the bare value $m$ (vector mesons). In approaching the critical value $m_c$ at $\beta$ fixed, there is a bifurcation of the energy gap: one branch follows the value $m$, while the new is much larger and it shows a more and more dominant weight. This phenomenon might be the sign of two important features: the long range correlation near the fixed point at $\beta \to \infty$ implied by the low energy gap and the screening (or confining) mechanisms across the $m=m_c$ associated to the larger gap. The I=0, J=0,1 gaps are of the same order of magnitude, typically larger than the I=1, J=1 gap (for $m>>m_c$). For $m\sim m_c$ both I=0 gaps have a dramatic drop with minima near the value $m$. This behavior might correspond to the formation of I=0 bound states both in the J=0 and J=1 channels

Metamorphosis versus Decoupling in Nonabelian Gauge Theories at Very High Energies

In the present paper we study the limit of zero mass in nonabelian gauge theories both with Higgs mechanism and in the nonlinear realization of the gauge group (Stueckelberg mass). We argue that in the first case the longitudinal modes undergo a metamorphosis process to the Goldstone scalar modes, while in the second we guess a decoupling process associated to a phase transformation. The two scenarios yield strikingly different behaviors at high energy, mainly ascribed to the presence of a massless Higgs doublet among the physical modes in the case of Higgs mechanism (i.e. not only the Higgs boson). The aim of this work is to show that the problem of unitarity at high energy in nonabelian gauge theory with no Higgs boson can open new perspectives in quantum field theory.Comment: Article, 31 pages. Typos removed and Ref. 7, 32 added. Revised argument in sections 4,9,10, results unchange

Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example

The renormalization procedure of the non-linear SU(2) sigma model in D=4 proposed in hep-th/0504023 and hep-th/0506220 is here tested in a truly non-trivial case where the non-linearity of the functional equation is crucial. The simplest example, where the non-linear term contributes, is given by the two-loop amplitude involving the insertion of two \phi_0 (the constraint of the non-linear sigma model) and two flat connections. In this case we verify the validity of the renormalization procedure: the recursive subtraction of the pole parts at D=4 yields amplitudes that satisfy the defining functional equation. As a by-product we give a formal proof that in D dimensions (without counterterms) the Feynman rules provide a perturbative symmetric solution.Comment: Latex, 3 figures, 19 page

Direct Algebraic Restoration of Slavnov-Taylor Identities in the Abelian Higgs-Kibble Model

A purely algebraic method is devised in order to recover Slavnov-Taylor identities (STI), broken by intermediate renormalization. The counterterms are evaluated order by order in terms of finite amplitudes computed at zero external momenta. The evaluation of the breaking terms of the STI is avoided and their validity is imposed directly on the vertex functional. The method is applied to the abelian Higgs-Kibble model. An explicit mass term for the gauge field is introduced, in order to check the relevance of nilpotency. We show that, since there are no anomalies, the imposition of the STI turns out to be equivalent to the solution of a linear problem. The presence of ST invariants implies that there are many possible solutions, corresponding to different normalization conditions. Moreover, we find more equations than unknowns (over-determined problem). This leads us to the consideration of consistency conditions, that must be obeyed if the restoration of STI is possible.Comment: 10 pages, Latex and packages amsfonts, amssymb and amsth