t Hooft mechanism of confinement or dual Meissner effect
t Hooft mechanism of confinement or dual Meissner effect
t Hooft mechanism of confinement or dual Meissner effect
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Polyakov’s realization <strong>of</strong> <strong>confinement</strong><br />
d = 2 + 1 Ge<strong>or</strong>gi–Glashow model: Yang–Mills SU(2) fields interacting with the Higgs<br />
field in the triplet representation:<br />
⎧(<br />
) 2<br />
⎫<br />
∫ ⎪⎨ F a (<br />
S = d 3 ij<br />
x + 1<br />
⎪⎩ 4g 2 2<br />
D ab<br />
i φb) 2 [ 2 + λ (φ a ) 2 − v 2] 2<br />
⎪⎬<br />
⎪⎭ .<br />
’t <strong>Ho<strong>of</strong>t</strong>–Polyakov monopole is a local minimum <strong>of</strong> this action:<br />
{<br />
φ a = ∓n a vΦ(r), n a = xa 0, r → 0<br />
r , Φ(r) → 1, r → ∞<br />
A a i<br />
1 − R(r)<br />
= ǫ aij n j , R(r) →<br />
r<br />
{ 1, r → 0<br />
0, r → ∞<br />
Magnetic field strength, B i<br />
r→∞<br />
∼<br />
n i<br />
r2 , is that <strong>of</strong> the magnetic monopole !<br />
Confinement in the 3d Ge<strong>or</strong>gi–Glashow model D. Diakonov, L-12
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