More on ghost condensation in Yang-Mills theory: BCS versus Overhauser effect and the breakdown of the Nakanishi-Ojima annex SL(2,R) symmetry

Abstract

We analyze the ghost condensates <f^{abc}c^{b}c^{c}>, <f^{abc}\oc^{b}\oc^{c}> and <f^{abc}\oc^{b}c^{c}> in Yang-Mills theory in the Curci-Ferrari gauge. By combining the local composite operator formalism with the algebraic renormalization technique, we are able to give a simultaneous discussion of <f^{abc}c^{b}c^{c}>, <f^{abc}\oc^{b}\oc^{c}> and <f^{abc}\oc^{b}c^{c}>, which can be seen as playing the role of the BCS, respectively Overhauser effect in ordinary superconductivity. The Curci-Ferrari gauge exhibits a global continuous symmetry generated by the Nakanishi-Ojima (NO) algebra. This algebra includes, next to the (anti-)BRST transformation, a SL(2,R) subalgebra. We discuss the dynamical symmetry breaking of the NO algebra through these ghost condensates. Particular attention is paid to the Landau gauge, a special case of the Curci-Ferrari gauge.

33 pages, 2 eps figures. v2: version published in JHEP, author added, error in potential corrected. Results and conclusions unchanged

References in corpus (27)

• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• The three-loop QCD $\beta$-function and anomalous dimensions
• Local BRST cohomology in gauge theories
• On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
• Non-perturbative Landau gauge and infrared critical exponents in QCD
• On the Significance of the Quantity "A Squared"
• Vacuum condensate of mass dimension 2 as the origin of mass gap and quark confinement
• On the Emerging Phenomenology of <(A_μ)^2>
• Testing Landau gauge OPE on the Lattice with a $<A^2>$ Condensate
• The non-perturbative groundstate of Q.C.D and the local composite operator A_mu^2
• Gluon propagators and quark confinement
• Dense QCD : Overhauser or BCS Pairing ?
• Three loop MSbar renormalization of the Curci-Ferrari model and the dimension two BRST invariant composite operator in QCD
• Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
• Lattice calculation of $1/p^2$ corrections to ${\alpha }_s$ and of ${\Lambda }_{\mathrm{QCD}}$ in the $\widetilde{MOM}$ scheme
• Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory
• Abelian dominance in low-energy Gluodynamics due to dynamical mass generation
• Instantons and $<A^2>$ Condensate
• CMB Anisotropy from Baryogenesis by a Scalar Field
• The Gluon Propagator without lattice Gribov copies on a finer lattice
• A determination of <A^2> and the non-perturbative vacuum energy of Yang-Mills theory in the Landau gauge
• On the SL(2,R) symmetry in Yang-Mills Theories in the Landau, Curci-Ferrari and Maximal Abelian Gauge
• A new start for local composite operators
• Defining < A^2 > in the finite volume hamiltonian formalism
• The `BRST-invariant' Condensate of Dimension Two in QCD
• Ghost condensates in Yang-Mills theories in nonlinear gauges
• Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

Cited by in corpus (24)

• Gauge bosons at zero and finite temperature
• An analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
• Dynamical gluon mass generation from <A^2> in linear covariant gauges
• Infrared Features of the Landau Gauge QCD
• The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory
• A study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon
• More on the renormalization of the horizon function of the Gribov-Zwanziger action and the Kugo-Ojima Green function(s)
• Effects of the quark field on the ghost propagator of Lattice Landau Gauge QCD
• Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
• Spontaneous Breaking of the BRST Symmetry in the ABJM theory
• Infrared features of unquenched finite temperature lattice Landau gauge QCD
• Ghost condensation on the lattice
• Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
• A combined study of the gluon and ghost condensates <A^2> and <epsilon^{abc} cbar^b c^c> in Euclidean SU(2) Yang-Mills theory in the Landau gauge
• Boundary Effects in Super-Yang-Mills Theory
• Noether Theorem and Nilpotency Property of the (Anti-)BRST Charges in the BRST Formalism: A Brief Review
• Nonperturbative ghost dynamics in the maximal Abelian gauge
• Spontaneous breaking of nilpotent symmetry in boundary BLG theory
• Brane cosmology in the Horava-Witten heterotic M-Theory on $S^1/Z_2$
• Nilpotent Charges in an Interacting Gauge Theory and an N = 2 SUSY Quantum Mechanical Model: (Anti-)Chiral Superfield Approach
• Nilpotent Symmetries and Curci-Ferrari Type Restrictions in 2D Non-Abelian Gauge Theory: Superfield Approach
• Some Novel Features in 2D Non-Abelian Theory: BRST Approach
• Slavnov-Taylor1.0: A Mathematica package for computation in BRST formalism
• Nilpotent (Anti-)BRST and (Anti-)co-BRST Symmetries in 2D non-Abelian Gauge Theory: Some Novel Observations