t Hooft mechanism of confinement or dual Meissner effect

More documents

Recommendations

Info

At large distances from monopoles only colour A 3 i Stokes theorem: ∫ W = Tr exp i d 2 S i B 3 i component survives =⇒ can use the τ 3 2 = e i 2 Φ + e − i 2 Φ , where Φ = ∫ d 2 S i B 3 i is the flux of the magnetic field created by monopoles and antimonopoles in the plasma, through the surface spanned over the Wilson loop. Wilson ( loop averaged over the ensemble of monopoles: have to plunge the source term ∫ ) i exp 2 d 2−→ S·−→ B into the partition function, and integrate over all possible magnetic fields. For large loops (say, lying in the z =0 plane), one can use the saddle-point method and find the ‘best’ fields −→ B, ψ minimizing the energy together with the surface source: B i (x, y, z) = δ iz B(z), ψ = ψ(z), Confinement in the 3d Georgi–Glashow model D. Diakonov, L-12
1 g 2B(z) + i 4π i dB dz for x, y inside the contour. The solution: dψ dz = i 2 δ(z), − 8πζ sin ψ = 0, e −µ|z| B = i g2 µ π 1 + e −2µ|z|, ( ψ = 4 sign(z) atan e −µ|z|) . The solution corresponds to a purely imaginary double layer of monopoles around the surface. String tension < W > = exp (−σ Area) , Confinement in the 3d Georgi–Glashow model D. Diakonov, L-12
Page 1 and 2: Mandelstam - Polyakov - ’t Hooft
Page 3 and 4: x = rm W , κ = λ e . E = Lv 2 ∫
Page 5 and 6: Action = v g w ( mH m W ) ≫ 1, w(
Page 7 and 8: Monopole interactions One can add u
Page 9 and 10: = exp − 1 2 4π g 2 ∫ ∫ = exp
Page 11 and 12: Average monopole density: ¯N V = 1
Page 13: Unusual: div B 3 = −4πρ, curl B
Page 17: Best dreams fulfilled! [A. Polyakov

t Hooft mechanism of confinement or dual Meissner effect

Create successful ePaper yourself

Delete template?

Save as template?