Yang–Mills theory in Landau gauge as a liquid crystal

Abstract

Using a spin-charge separation of the gluon field in the Landau gauge we show that the SU (2) Yang-Mills theory in the low-temperature phase can be considered as a nematic liquid crystal. The ground state of the nematic crystal is characterized by the A 2 condensate of the gluon field. The liquid crystal possesses various topological defects (instantons, monopoles and vortices) which are suggested to play a role in non-perturbative features of the theory.Separation of degrees of freedom is a useful analytical tool which is widely used in various physical applications. For example, the spin-charge decomposition (often referred to as the slave-boson formalism [1]) of the strongly correlated electrons is a popular technique invoked to describe a low-temperature physics of the high-T c cuprate superconductors [2]. According to the slave-boson formalism the electron creation operator c † iσ is represented as the product of two operators,where i is the lattice site and σ =↑, ↓ is the spin index. The operator f † iσ creates a chargeless spin-1/2 fermion state ("spinon") while the operator b i annihilates a charged spin-0 boson state ("holon"). Physically, the electron is represented as a composite of the spinon particle (which carries information about the spin of the electron) and the holon particle (which knows about the electron charge). The decomposition conserves the total number of the degrees of freedom because of the constraint(1) the states with double occupancy are disregarded for simplicity.The local nature of the spin-charge decomposition (1) leads to an emergence of an internal compact U(1) gauge symmetry realized in the form of the gauge transformationsCertain properties of the high-T c superconductors can be described [2,3] by U(1) gauge models which are utilizing the mentioned internal gauge symmetry. These gauge models are treatable within the mean field approach which predicts a rich phase structure. In particular, the d-wave high-T c superconductor is suggested [3] to be realized as a phase in which the spinon pairing,, is accompanied with a spontaneous breaking of the internal U(1) symmetry by the holon condensate:The presence and the subsequent spontaneous breaking of the internal gauge symmetry may have important physical consequences if even this symmetry is not realized in the original formulation of the theory. Quantum Chromodynamics is another example of a strongly interacting system in which the breaking of the internal symmetry may play an essential role. Long time ago it was

Non-associative slave-boson decomposition

“…In Ref. [3] the similar construction (spin-charge separation) for the gauge boson is offered as well. The physical ground is that in both cases we are dealing with strong interactions: between electrons in High-T c superconductivity and gauge bosons in quantum chromodynamics.…”

Spin-Charge Separation for the Su(3) Gauge Theory

“…Absolutely by the same way as in Ref. 6 one can calculate the ground state of the nematic associated with the Yang-Mills theory (13)-(15). If we introduce the eigenvalues of the matrix χ = diag{χ 1 , χ 2 , χ 3 }, the ground state χ = χ 0 is defined as…”

“…[2][3][4][5] In Ref. 6 the idea presented that is an analogy may exist between the SU(2) Yang-Mills theory in the low-temperature phase and a nematic liquid crystal. The idea is based on a spin-charge separation of the gluon field in the Landau gauge.…”

Liquid crystal defects of Yang-Mills theory in Landau gauge

“…Recently, attempts to approach the confinement problem in terms of particular gluon configurations in this gauge were made in Ref. [4,5,6,7]. It was shown numerically [4] that in the Landau gauge the formation of the confining string is caused by magnetic displacement currents.…”