A world-line framework for 1D Topological Conformal sigma-models

Abstract

We use world-line methods for pseudo-supersymmetry to construct $sl(2|1)$-invariant actions for the $(2,2,0)$ chiral and ($1,2,1)$ real supermultiplets of the twisted $D$-module representations of the $sl(2|1)$ 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 $\lambda =-\frac{1}{2}$. We also present, generalizing previous works, the $D$-module representations of one-dimensional superconformal algebras induced by $\mathcal{N}=(p,q)$ pseudo-supersymmetry acting on $(k,n,n-k)$ supermultiplets. Besides $sl(2|1)$, 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 $\lambda$.

19 pages; three references added

References in corpus (4)

• Superconformal mechanics in SU(2|1) superspace
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• Four types of (super)conformal mechanics: D-module reps and invariant actions
• Superconformal quantum mechanics and the exterior algebra

Cited by in corpus (2)

• Classification of minimal ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie (super)algebras and some applications
• An Angular Dependent Supersymmetric Quantum Mechanics with a ${\mathbf{Z}}_2$-invariant Potential