Properties of semi-chiral superfields

Abstract

Whenever the N = (2, 2) supersymmetry algebra of non-linear σ-models in two dimensions does not close off-shell, a holomorphic two-form can be defined. The only known superfields providing candidate auxiliary fields to achieve an off-shell formulation are semi-chiral fields. Such a semi-chiral description is only possible when the two-form is constant. Using an explicit example, hyperKähler manifolds, we show that this is not always the case. Finally, we give a concrete construction of semi-chiral potentials for a class of hyper-Kähler manifolds using the duality exchanging a pair consisting of a chiral and a twistedchiral superfield for one semi-chiral multiplet.

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.…”

A potential for generalized Kähler geometry

“…and find the metric and B-field using this matrix as follows [14] (cf. 4.24) We assume that in a neighborhood of x 0 , the ranks of π ± are constant, and as result, the rank of σ is constant.…”

The biHermitian topological sigma model

“…In a classic paper, Gates, Hull and Roček [3] showed that, for a 2-dimensional sigma model, the most general target space geometry allowing for (2, 2) supersymmetry was biHermitian or Kaehler with torsion geometry. This is characterized by a Riemannian metric g ab , two generally non commuting complex structures K ± a b and a closed 3-form H abc , such that g ab is Hermitian with respect to both the K ± a b and the K ± a b are parallel with respect to two different metric connections with torsion proportional to ±H abc [4][5][6][7]. This geometry is more general than that considered by Witten, which corresponds to the case where K + a b = ±K − a b and H abc = 0.…”