Quantum and string shape fluctuations in the dual monopole Nambu–Jona–Lasinio model with dual Dirac strings

Abstract

The magnetic monopole condensate is calculated in the dual Monopole NambuJona-Lasinio model with dual Dirac strings suggested in Refs. [1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole-antimonopole collective excitation field. The integration over quantum fluctuations of the dual-vector monopole-antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate. * Supported by the Fonds zur Förderung der wissenschaftlichen Forschung, Project P12495-TPH. †

Confinement potential in the dual monopole Nambu–Jona–Lasinio model with dual Dirac strings

“…This corresponds to the London limit M σ = 2 M ≫ M C in the dual Higgs model with dual Dirac strings [5][6][7]. The inequality M σ ≫ M C means also that in the MNJL model we deal with Dual Superconductivity of type II [4]. In the tree σ-field approximation the r.h.s.…”

“…The dual Monopole Nambu-Jona-Lasinio model (MNJL) with dual Dirac strings as continuum space-time analogy of Compact Quantum Electrodynamics (CQED) [1] has been formulated in Ref. [2][3][4]. The MNJL-model is based on a Lagrangian, invariant under magnetic U(1) symmetry, with massless magnetic monopoles self-coupled through a local four-monopole interaction [2,3]:…”

“…The self-interactions L int [σ(x)] provide σ-field loop contributions and can be dropped out in the tree σ-field approximation accepted in Refs. [2][3][4]. The tree σ-field approximation can be justified keeping massive magnetic monopoles very heavy, i.e.…”

“…In our consideration quarks and antiquarks are classical point-like particles with masses m q = m q = m, electric charges Q q = −Q q = Q, and trajectories X ν q (τ ) and X ν q (τ ), respectively. The field strength F µν (x) is defined [2][3][4] as…”

“…, and * dC µν (x) is the dual version, i.e., * dC µν (x) = 1 2 ε µναβ dC αβ (x) (ε 0123 = 1). The dual "chromo"-electric field strength E µν (x), induced by a dual Dirac string, is defined following [2][3][4] as…”