On microscopic structure of the QCD vacuum

Abstract

We propose a new class of regular stationary axially symmetric solutions in a pure QCD which correspond to monopole-antimonopole pairs at macroscopic scale. The solutions represent vacuum field configurations which are locally stable against quantum gluon fluctuations in any small spacetime vicinity. This implies that the monopole-antimonopole pair can serve as a structural element in microscopic description of QCD vacuum formation through the monopole pair condensation.

Color structure of quantum SU(N) Yang-Mills theory

“…where p 1 , q 1 are number parameters. One can verify that ansatz (42) is consistent with Yang-Mills equations of motion, and symmetric under Weyl permutations in six dimensional spaces spanned by T 1,4,6,9,11,13 and T 2,5,7,10,12,14 and in the root space spanned by six linear combinations of Cartan generators r p α T α . One can reduce the ansatz and construct a minimal Weyl symmetric ansatz with four independent fields…”

“…A general ansatz for magnetic type time-dependent solutions contains four Abelian potentials A 3,8,15,24 ϕ corresponding to the maximal Abelian subgroup of SU (5), ten Abelian potentials A p ϕ with an internal index p = (1,4,6,9,11,13,16,18,20,22) which corresponds to coset generators T 1,4,6,9,11,13,16,18,20,22 and it is used also for counting the root vectors, and ten off-diagonal vector fields A ṗ i (i = 0, 1, 2) corresponding to index values ṗ = (2, 5, 7, 10, 12, 14, 17, 19, 21, 23) corresponding to coset generators T 2,5,7,10,12,14,17,19,21,23 . A minimal ansatz is reduced by imposing reduction constraints…”

“…The Lagrangian can be treated as a non-linear realization of U (1) gauge theory for the vector field K 0,1,2,3 in the Lorenz type gauge, and it reproduces the equations (9)(10)(11)(12). It has been proved that stationary solutions satisfying equations (9)(10)(11)(12) are stable under vacuum gluon fluctuations [13]. The solutions are the only known classical solutions which describe a stable vacuum in a pure Yang-Mills theory in quasiclassical approximation.…”

“…A general Weyl symmetric ansatz contains three Abelian magnetic fields A 3,8,15 ϕ in the Cartan space, additional six independent Abelian fields A 1,4,6,9,11,13 ϕ in the coset subspace spanned by generators T 1,4,6,9,11,13 and eighteen off-diagonal fields K i , Q i , S i , P i , T i , R i (i = 0, 1, 2)…”

Microscopic vacuum structure in a pure QCD

“…A generalized axially symmetric Dashen-Hasslacher-Neveu (DHN) ansatz [15,16] for non-vanishing components of the gauge potential A a µ (r, θ, t) in the holonomic basis reads…”