Confinement, brane symmetry and the Julia-Toulouse approach for condensation of defects

Abstract

In this work the phenomenon of charge confinement is approached in various contexts. An universal criterion for the identification of this phenomenon in Abelian gauge theories is suggested: the so-called spontaneous breaking of the brane symmetry. This local symmetry has its most common manifestation in the Dirac string ambiguity present in the electromagnetic theory with monopoles. The spontaneous breaking of the brane symmetry means that the Dirac string becomes part of a brane invariant observable which hides the realization of such a symmetry and develops energy content in the confinement regime. The establishment of this regime can be reached through the condensation of topological defects. The effective theory of the confinement regime can be obtained with the Julia-Toulouse prescription which (originally introduced as the dual mechanism to the Abelian Higgs Mechanism) is generalized in this paper in order to become fully compatible with Elitzur's theorem and describe more general condensates which may break Lorentz and discrete spacetime symmetries. This generalized approach for the condensation of defects is presented here through a series of different applications.

Vanishing DC holographic conductivity from a magnetic monopole condensate

“…In doing so, we have effectively promoted the kinetic term with magnetic defects for the A µ field to a mass term for the K µν field. As mentioned above, the condensation of topological currents constitutes a type of mass generation mechanism [29,30,34,[37][38][39] and the rank jump phenomenon is a general signature of this mass gap generation in the picture where the condensing currents couple non-minimally to p-form Abelian gauge fields [29,30,34].…”

“…This change in the number of the degrees of freedom going from the bulk phase with diluted monopoles, described by the Maxwell action non-minimally coupled to magnetic defects, to the bulk phase with condensed monopoles (whose lowest lying excitations are described by the massive 2-form field) is associated with the mass gap generation mechanism triggered by the condensation of these monopoles. Furthermore, it is also important to point out that for any number of spacetime dimensions where a non-minimal coupling structure can be defined with respect to a 1-form gauge field, 14 a description of the lowest lying modes of a phase characterized by a condensate of magnetically charged defects can always be given directly in terms of a massive 2-form field [30,34]. 13 To make clear the comparison between our action (2.1) and eq.…”

“…which would give us a version of the action (2.3) with a constant mass for the 2-form field [30,34]. However, as discussed in the previous sections, we need an effective mass for this 2-form bulk field that varies with the holographic coordinate and goes to zero at the boundary in order to properly compute the holographic conductivity associated to the 2-point retarded correlation function of a conserved vector current operator at the boundary QFT sourced by the boundary value of the 2-form field.…”

“…In our action (2.1), the field M is then identified with the ratio between this modulus and its expectation value. 13 It is also important to observe that the the Maxwell field in a 4-dimensional bulk has two degrees of freedom while the number of degrees of freedom of a massive 2-form field in the same dimensionality is three, which may be easily traced back to the fact that a massive 2-form field in four dimensions is electromagnetically dual to a massive vector field [18,34]. This change in the number of the degrees of freedom going from the bulk phase with diluted monopoles, described by the Maxwell action non-minimally coupled to magnetic defects, to the bulk phase with condensed monopoles (whose lowest lying excitations are described by the massive 2-form field) is associated with the mass gap generation mechanism triggered by the condensation of these monopoles.…”

“…Thus, the condensation of topological defects constitutes a mass gap generation mechanism whose general signature is the so-called "rank jump phenomenon": a massless Abelian p-form describing the system in the phase with diluted defects gives place to a new effective massive (p + 1)-form describing the system in the condensed phase. Quevedo and Trugenberger refer to this as the "Julia-Toulouse mechanism" (JTM) and, more recently, some of us generalized the JTM in various aspects and applied it to many different physical systems [31][32][33][34][35][36][37][38][39][40][41].…”