Generalizations of NLSM

Abstract

In this chapter we give several different generalizations of the NLSM concept, by relaxing the assumptions made about the NLSM in the Introduction (Chap. 1). In Sect. 9.1 we consider the 4d, N = 2 NLSM with the ALE target spaces, and demonstrate that the Eguchi-Hanson 4d, N = 2 NLSM with a non-vanishing N = 2 central charge gives rise to dynamical generation of the composite N = 2 vector gauge multiplet, in one-loop perturbation theory [579, 580]. The composite N = 2 vector multiplet is identified with the zero modes of the superstring ending on a D6-brane. In Sect. 9.2 we relax another assumption that the NLSM fields should be represented by scalars or supersymmetric scalar multiplets. The NLSM (e.g., with an n-sphere as the target space) is often related to spontaneous breaking of internal symmetry (e.g., the O(n) rotational symmetry). A spontaneous breakdown of internal symmetry can be accomplished by starting with a linear realization of the symmetry (e.g. in terms of the scalar n-field) and then imposing a non-linear constraint (e.g., by defining the O(n) NLSM of the n-field by assigning its values to the n-sphere). This concept can be further generalized to partial (1/2) spontaneous supersymmetry breaking with a vector supermultiplet of Goldstone modes [581]. The corresponding Goldstone action can be interpreted as the gauge-fixed D-brane action that can be put into NLSM-type form by using a non-linear superfield constraint (Sect. 9.2).