Off-shell formulation of N = 2 non-linear σ-models

Abstract

We study d = 2, N = (2, 2) non-linear σ-models in (2, 2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted chiral and semi-chiral ones. We study the resulting σ-models and we speculate on the possibility that all (2, 2) non-linear σ-models can be described using these fields. We apply the results to two examples: the SU (2) × U (1) and the SU (2) × SU (2) WZW model. Pending upon the choice of complex structures, the former can be described in terms of either one semi-chiral multiplet or a chiral and a twisted chiral multiplet. The latter is formulated in terms of one semi-chiral and one twisted chiral multiplet. For both cases we obtain the potential explicitely.

On dimensional extension of supersymmetry: from worldlines to worldsheets

“…As shown in the appendix, this implies that the real component (super)fields depicted by the nodes of the Adinkra may be complexified simultaneously with the two real components of D α+ . The appendix also proves that the supermultiplet depicted by (3.7) is one of the two semi-chiral supermultiplets [31,33], the other one obtained by swapping the assignment to the edges D α+ ↔ D . …”

“…Worldsheet dimensional extension is thus a stepping stone towards dimensional extension to higher-dimensional spacetimes. Of course, worldsheet supersymmetry is also important in its own right [23][24][25][26] and affords comparison with numerous known results; see [2,5,[27][28][29][30][31][32][33][34][35], to name but a few.…”

“…It is possible to complexify simultaneously the component superfields [31,33], and we now turn to prove this.…”

“…The semichiral supermultiplet is defined as a complex intact (2, 2)-superfield subject to the single complex superdifferential constraint [31,33]:…”

Superstrings with intrinsic torsion

“…It is sometimes incorrectly stated in the literature (see for instance [55,56,57]) that Π, defined by (C.4), is integrable if and only if the two commuting almost complex structures are integrable. A concrete class of counter-example is provided by the geometry (7.2) for generic instantons G. This geometry has an SU (2) structure, built from the ǫ − Killing spinors, which can be specified by two SU ( Computing the corresponding Nijenhuis tensor, we find that it has the non-zero components…”