Dual superconducting model
Encyclopedia
In the theory of quantum chromodynamics
, dual superconductor models attempt to explain confinement
of quark
s in terms of an electromagnetic dual theory of superconductivity
.
In an electromagnetic dual theory the roles of electric
and magnetic field
s are interchanged. The BCS theory
of superconductivity explains superconductivity as the result of the condensation electric chargers to cooper pair
s. In a dual superconductor an analogous effect occurs through the condensation of magnetic charges (also called magnetic monopole
s). In ordinary electromagnetic theory, no monopoles have been shown to exist. However, in quantum chromodynamics — the theory of colour charge which explains the strong interaction
between quarks — the colour charges can be view as (non-abelian) analogues of electric charges and corresponding magnetic monopoles are known to exist. Dual superconductor models posit that condensation of these magnetic monopoles in a superconductive state explains colour confinement — the phenomenon that only neutrally coloured bound states are observed at low energies.
Qualitatively, confinement in dual superconductor models can be understood as a result of the dual to the Meissner effect
. The Meissner effect says that a superconducting metal will try to expel magnetic field lines from its interior. If a magnetic field is forced to run through the superconductor, the field lines are compressed in magnetic flux tubes. In a dual superconductor the roles of magnetic and electric fields are exchanged and the Meissner effect tries to expel electric field lines. Quarks and antiquarks carry opposite colour charges, and for a quark–antiquark pair 'electric' field lines run from the quark to the antiquark. If the quark–antiquark pair are immersed in a dual superconductor, then the electric field lines get compressed to a flux tube. The energy associated to the tube is proportional to its length, and the potential energy of the quark–antiquark is proportional to their separation. A quark–antiquark will therefore always bind regardless of their separation, which explains why no unbound quarks are ever found.
Dual superconductors are described by (a dual to) the Landau–Ginzburg model, which is equivalent to the Abelian Higgs model.
The dual superconductor model is motivated by several observations in calculations using lattice gauge theory
. The model, however, also has some shortcomings. In particular, although it confines coloured quarks, it fails to confine colour of some gluon
s, allowing coloured bound states at energies observable in particle colliders.
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
, dual superconductor models attempt to explain confinement
Colour confinement
Color confinement, often simply called confinement, is the physics phenomenon that color charged particles cannot be isolated singularly, and therefore cannot be directly observed. Quarks, by default, clump together to form groups, or hadrons. The two types of hadrons are the mesons and the baryons...
of quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s in terms of an electromagnetic dual theory of superconductivity
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
.
In an electromagnetic dual theory the roles of electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s are interchanged. The BCS theory
BCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
of superconductivity explains superconductivity as the result of the condensation electric chargers to cooper pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
s. In a dual superconductor an analogous effect occurs through the condensation of magnetic charges (also called magnetic monopole
Magnetic monopole
A magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...
s). In ordinary electromagnetic theory, no monopoles have been shown to exist. However, in quantum chromodynamics — the theory of colour charge which explains the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
between quarks — the colour charges can be view as (non-abelian) analogues of electric charges and corresponding magnetic monopoles are known to exist. Dual superconductor models posit that condensation of these magnetic monopoles in a superconductive state explains colour confinement — the phenomenon that only neutrally coloured bound states are observed at low energies.
Qualitatively, confinement in dual superconductor models can be understood as a result of the dual to the Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...
. The Meissner effect says that a superconducting metal will try to expel magnetic field lines from its interior. If a magnetic field is forced to run through the superconductor, the field lines are compressed in magnetic flux tubes. In a dual superconductor the roles of magnetic and electric fields are exchanged and the Meissner effect tries to expel electric field lines. Quarks and antiquarks carry opposite colour charges, and for a quark–antiquark pair 'electric' field lines run from the quark to the antiquark. If the quark–antiquark pair are immersed in a dual superconductor, then the electric field lines get compressed to a flux tube. The energy associated to the tube is proportional to its length, and the potential energy of the quark–antiquark is proportional to their separation. A quark–antiquark will therefore always bind regardless of their separation, which explains why no unbound quarks are ever found.
Dual superconductors are described by (a dual to) the Landau–Ginzburg model, which is equivalent to the Abelian Higgs model.
The dual superconductor model is motivated by several observations in calculations using lattice gauge theory
Lattice gauge theory
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum electrodynamics, quantum chromodynamics and the Standard...
. The model, however, also has some shortcomings. In particular, although it confines coloured quarks, it fails to confine colour of some gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
s, allowing coloured bound states at energies observable in particle colliders.