A world-line framework for 1D topological conformal sigma-models

作者：Baulieu L^*; Holanda N L; Toppan F

来源：Journal of Mathematical Physics, 2015, 56(11): 113507.

DOI：10.1063/1.4935851

We use world-line methods for pseudo-supersymmetry to construct sl(2 vertical bar 1)-invariant actions for the (2, 2, 0) chiral and (1, 2, 1) real supermultiplets of the twisted D-module representations of the sl(2 vertical bar 1) superalgebra. The derived one-dimensional topological conformal sigma-models are invariant under nilpotent operators. The actions are constructed for both parabolic and hyperbolic/trigonometric realizations (with extra potential terms in the latter case). The scaling dimension lambda of the supermultiplets defines a coupling constant, 2 lambda + 1, the free theories being recovered at lambda = -1/2. We also present, generalizing previous works, the D-module representations of one-dimensional superconformal algebras induced by N = (p, q) pseudo-supersymmetry acting on (k, n, n - k) supermultiplets. Besides sl(2 vertical bar 1), we obtain the superalgebras A(1,1), D(2, 1; alpha), D(3,1), D(4,1), A(2,1) from (p, q) = (1,1), (2,2), (3,3), (4,4), (5,1), at given k, n and critical values of lambda.