Geometry of theN= 2 supersymmetric sigma model with Euclidean worldsheet

Abstract

We investigate the target space geometry of supersymmetric sigma models in two dimensions with Euclidean signature, and the conditions for N = 2 supersymmetry. For a real action, the geometry for the N = 2 model is not the generalized Kähler geometry that arises for Lorentzian signature, but is an interesting modification of this which is not a complex geometry.

Euclidean pseudoduality and boundary conditions in sigma models

“…The sigma model with target space M, metric g and antisymmetric 2-form b is denoted by (M, g, b) and has the action in the Euclidean worldsheet Σ [12]…”

“…These two equations are intriguing and lead to take advantage of equations of motion and the desired integrability conditions for the pseudoduality equations. As opposed to the method followed in [9,10] we first and foremost wedge the first equation (11) by dτ and the second (12) by dσ, and use x τ σ = x στ (similarlyx τ σ =x στ ) to get…”