15847137
Physical unitarity for massive non-Abelian gauge theories in the Landau gauge: Stueckelberg and Higgs
We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stuckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor identities should be respected!) and we devote the paper to the study of the space of the unphysical modes. We find that the theory is unitary only under the hypothesis that the 1-PI two-point function of the vector mesons has no poles (at p2 = 0). This normalization condition might be rather crucial in the very definition of the theory. With all these provisos the theory is unitary. The proof of unitarity is given both in a form that allows a direct transcription in terms of Feynman amplitudes (cutting rules) and in the operatorial form. The same arguments and conclusions apply verbatim to the case of non-abelian gauge theories where the mass of the vector meson is generated via Higgs mechanism. To the best of our knowledge, there is no mention in the literature on the necessary condition implied by physical unitarity.
118662569
Background field dependence from the Slavnov-Taylor identity in (non-perturbative) Yang-Mills theory
We show that in Yang-Mills theory the Slavnov-Taylor (ST) identity, extended in the presence of a background gauge connection, allows to fix in a unique way the dependence of the vertex functional on the background, once the 1-PI amplitudes at zero background are known. The reconstruction of the background dependence is carried out by purely algebraic techniques and therefore can be applied in a non-perturbative scheme (e.g. on the lattice or in the Schwinger-Dyson approach), provided that the latter preserves the ST identity. The field-antifield redefinition, which replaces the classical background-quantum splitting when quantum corrections are taken into account, is considered on the example of an instanton background in SU(2) Yang-Mills theory.
13904067
Path-integral over non-linearly realized groups and hierarchy solutions
The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.
17373833
Comments on the Equivalence between Chern-Simons Theory and Topological Massive Yang-Mills Theory in 3D
The classical formal equivalence upon a redefinition of the gauge connection between Chern-Simons theory and topological massive Yang-Mills theory in three-dimensional Euclidean space-time is analyzed at the quantum level within the BRST formulation of the Equivalence Theorem. The parameter controlling the change in the gauge connection is the inverse λ of the topological mass. The BRST differential associated with the gauge connection redefinition is derived and the corresponding Slavnov-Taylor (ST) identities are proven to be anomaly-free. Hence they can be restored order by order in the loop expansion by a recursive choice of non-invariant counterterms. The Green functions of local operators constructed only from the (λ-dependent) transformed gauge connection, as well as those of BRST invariant operators, are shown to be independent of the parameter λ, as a consequence of the validity of the ST identities. The relevance of the antighost-ghost fields (μ,cμ), needed to take into account at the quantum level the jacobian of the change in the gauge connection, is analyzed. Their role in the identification of the physical states of the model within conventional perturbative gauge theory is discussed. It is shown that (μ,cμ) prove to be essential in keeping the correspondence between the degrees of freedom of the theory at λ = 0 (Chern-Simons theory) and at λ≠0.
6786885
The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model
Abstract
In perturbation theory we study the matching in four dimensions between the linear sigma model in the large mass limit and the renormalized nonlinear sigma model in the recently proposed flat connection formalism. We consider both the chiral limit and the strong coupling limit of the linear sigma model. Our formalism extends to Green functions with an arbitrary number of pion legs, at one loop level, on the basis of the hierarchy as an efficient unifying principle that governs both limits. While the chiral limit is straightforward, the matching in the strong coupling limit requires careful use of the normalization conditions of the linear theory, in order to exploit the functional equation and the complete set of local solutions of its linearized form.

1638696
FURTHER COMMENTS ON THE SYMMETRIC SUBTRACTION OF THE NONLINEAR SIGMA MODEL
Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled to the nonlinear sigma model constraint (flat connection formalism). The construction is based on a local functional equation, which overcomes the problems due to the presence (already at one loop) of nonchiral symmetric divergences. The subtraction procedure of the divergences in the loop expansion is performed by means of minimal subtraction of properly normalized amplitudes in dimensional regularization. In this paper we complete the study of this subtraction procedure by giving the formal proof that it is symmetric to all orders in the loopwise expansion. We provide further arguments on the issue that, within our subtraction strategy, only two parameters can be consistently used as physical constants.
13130827
Clustering of K-selected Galaxies at 2 < z < 3.5: Evidence for a Color-Density Relation
We study the clustering properties of K-selected galaxies at 2 2.3 distant red galaxies (DRGs) have r0 ~ 11 h-1 Mpc. Furthermore, contrary to findings for optically selected galaxies, K-selected galaxies that are faint in the R band cluster more strongly than brighter galaxies. These results suggest that a color-density relation was in place at z > 2; it will be interesting to see whether this relation is driven by galaxies with old stellar populations or by dusty star-forming galaxies. Irrespective of the cause, our results indicate that K-bright blue galaxies and K-bright red galaxies are fundamentally different, having different clustering properties. Using a simple model of one galaxy per halo, we infer halo masses ~5 × 1012 M☉ for K < 21 galaxies and ~2 × 1013 M☉ for DRGs. A comparison of the observed space density of DRGs to that of their host halos suggests large halo occupation numbers; however, this result conflicts with the lack of a strong small-scale excess in the angular correlation function. Using the predicted evolution of halo mass to investigate relationships between galaxy populations at different redshifts, we find that the z = 0 descendants of the galaxies considered here reside primarily in groups and clusters.