By Abhay Ashtekar
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Furthermore, for 4 /4, the extremum is a maximum and hence the Z-string is unstable. A very similar analysis has been done [70,81] for the =-string con"rming the result  that it is always unstable. (iii) W-condensation: There is also a well-known  instability to perturbations in the =-"elds alone called `=-condensationa. Application of this instability to the Z-string may be found in [107,124,125,6]. A heuristic argument goes as follows. 2eB ) s , (141) X where n"0, 1, 2,2 labels the Landau levels and p is the momentum along the z-axis.
Thus, embedded vortices belonging to a family are always unstable. erence is that the Z-string is known to terminate on magnetic monopoles but this is not true of the =-string. The =-string can terminate without any emanating electromagnetic "elds since it is entirely within the S;(2) sector of the GSW model. It is straightforward to embed domain walls in the GSW model. There are no embedded monopoles in the GSW model since there is no S;(2) subgroup that is broken to ;(1). 6. Electroweak strings in extensions of the GSW model Electroweak strings have been discussed in various extensions of the GSW model.
Therefore it must continue from within the string to beyond the terminus. E However, beyond the terminus, the Higgs is in its vacuum and the hypercharge magnetic "eld is massive. Then, if the massive hypercharge #ux was to continue beyond the string, it would cost an in"nite amount of energy and this is not possible. E The only means by which the hypercharge "eld can continue beyond the terminus is in combination with the S;(2) "elds such that it forms the massless electromagnetic magnetic "eld.
2D Quantum Gravity and SC at high Tc by Abhay Ashtekar