Wall-string junctions

Abstract

In Chapter 8 we reviewed the construction of D -brane prototypes in field theory. In string theory D branes are extended objects on which fundamental strings can end. To make contact with this string/brane picture one may address a question whether or not solitonic strings can end on the domain wall which localizes gauge fields. The answer to this question is yes. Moreover, the string endpoint plays a role of a charge with respect to the gauge field localized on the wall surface. This issue was studied in [215] in the sigma-model setup and in [217] for gauge theories at strong coupling. A solution for a 1/4-BPS wall-string junction in the N = 2 supersymmetric U(1) gauge theory at weak coupling was found in [142], while [37] deals with its non-Abelian generalization. Further studies of the wall-string junctions were carried out in [172] where all 1/4-BPS solutions to Eqs. (4.5.5) were obtained, and in [218, 231] where the energy associated with the wall-string junction (boojum) was calculated, and in [232, 228] where a quantum version of the effective theory on the domain wall world volume which takes into account charged matter (strings of the bulk theory) was derived. Below we will review the wall-string junction solutions and then briefly discuss how the presence of strings in the bulk modifies the effective theory on the wall.