Gauge dependence of one-particle irreducible (1-PI) amplitudes in SU(N) Yang-Mills theory is shown to be generated by a canonical flow with respect to (w.r.t.) the extended Slavnov-Taylor (ST) identity, induced by the transformation of the gauge para
meter under the BRST symmetry. For linear covariant gauges, the analytic expansion in the gauge parameter of 1-PI amplitudes is given in terms of coefficients evaluated in the Landau gauge and of derivatives w.r.t. the gauge parameter of the generating functional of the flow. An application to the gauge flow of the gluon propagator is considered.
We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in $D$ dimensions, based on the validity of a certain Local Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure under local left transform
ations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI) amplitudes (both on-shell and off-shell) can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed.
We clarify the derivation of high-energy QCD evolution equations from the fundamental gauge symmetry of QCD. The gauge-fixed classical action of the Color Glass Condensate (CGC) is shown to be invariant under a suitable BRST symmetry, that holds afte
r the separation of the gluon modes into their fast classical (background) part, the soft component and the semifast one, over which the one-step quantum evolution is carried out. The resulting Slavnov-Taylor (ST) identity holds to all orders in perturbation theory and strongly constrains the CGC effective field theory (EFT) arising from the integration of the soft modes. We show that the ST identity guarantees gauge-invariance of the EFT. It also allows to control the dependence on the gauge-fixing choice for the semifast modes (usually the lightcone gauge in explicit computations). The formal properties of the evolution equations valid in different regimes (BKFL, JIMWLK, ...) can be all derived in a unified setting within this algebraic approach.
We show that a powerful Slavnov-Taylor (ST) identity exists for the Effective Field Theory (EFT) of the Color Glass Condensate (CGC), allowing to control by purely algebraic means the full dependence on the background fields of the fast gluon modes,
as well as the correlators of the quantum fluctuations of the classical gluon source. We use this formalism to study the change of the background fast modes (in the Coulomb gauge), induced by the quantum corrections of the semi-fast gluons. We establish the evolution equation for the EFT of the CGC, which points towards an algebraic derivation of the JIMWLK equation. Being based on symmetry-arguments only, the approach can be used to extend the analysis to arbitrary gauges and to higher orders in the perturbation expansion of the EFT.
We consider a minimal nonlinearly realized electroweak theory where mass generation happens `a la Stueckelberg. Deformation of the nonlinearly realized gauge symmetry is controlled by functional methods. The Weak Power Counting allows to select uniqu
ely the Hopf algebra of the theory and gives definite predictions on the Beyond-the-Standard Model (BSM) sector of the theory: the latter includes one CP-odd and two charged physical scalars (in addition to the Higgs-like CP-even resonance). The model interpolates between a purely Stueckelberg and a Higgs scenario. It can be used in order to check whether the presence of a Stueckelberg mass component can already be excluded on the basis of the existing LHC7-8 data.
We show that it is possible to accommodate physical scalar resonances within a minimal nonlinearly realized electroweak theory in a way compatible with a natural Hopf algebra selection criterion (Weak Power Counting) and the relevant functional ident
ities of the model (Local Functional Equation, Slavnov-Taylor identity, ghost equations, b-equations). The Beyond-the-Standard-Model (BSM) sector of the theory is studied by BRST techniques. The presence of a mass generation mechanism `a la Stuckelberg allows for two mass invariants in the gauge boson sector. The corresponding t Hooft gauge-fixing is constructed by respecting all the symmetries of the theory. The model interpolates between the Higgs and a purely Stuckelberg scenario. Despite the presence of physical scalar resonances, we show that tree-level violation of unitarity in the scattering of longitudinally polarized charged gauge bosons occurs at sufficiently high energies, if a fraction of the mass is generated by the Stuckelberg mechanism. The formal properties of the physically favoured limit after LHC7-8 data, where BSM effects are small and custodial symmetry in the gauge boson sector is respected, are studied.
We show how to implement the background field method by means of canonical transformations and comment on the applications of the method to non-perturbative techniques in non-Abelian gauge theories. We discuss the case of the lattice in some details.
We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is nothing but a
direct field-theoretic generalization of the Lie transform of classical analytical mechanics, we comment on a number of possible applications, and in particular the non perturbative implementation of the background field method on the lattice, the background field formulation of the two particle irreducible formalism, and, finally, the formulation of the Schwinger-Dyson series in the presence of topologically non-trivial configurations.
A consistent strategy for the subtraction of the divergences in the nonlinearly realized Electroweak Model in the loop expansion is presented. No Higgs field enters into the perturbative spectrum. The local functional equation (LFE), encoding the inv
ariance of the SU(2) Haar measure under local left SU(2) transformations, the Slavnov-Taylor identity, required in order to fulfill physical unitarity, and the Landau gauge equation hold in the nonlinearly realized theory. The quantization is performed in the Landau gauge for the sake of simplicity and elegance. The constraints on the admissible interactions arising from the Weak Power-Counting (WPC) are discussed. The same symmetric pattern of the couplings as in the Standard Model is shown to arise, as a consequence of the defining functional identities and the WPC. However, two independent mass invariants in the vector meson sector are possible, i.e. no tree-level Weinberg relation holds between the Z and W mass. Majorana neutrino masses can be implemented in the nonlinearly realized Electroweak Model in a way compatible with the WPC and all the symmetries of the theory.
