Diverse ${\cal N} =(4,4)$ Twisted Multiplets in ${\cal N} = (2,2)$ Superspace

TL;DR

This paper classifies four types of ${ m N}=(4,4)$ twisted supermultiplets in ${ m N}=(2,2)$ superspace, analyzing their transformation properties, sigma model actions, and interactions, revealing that different types are mostly independent except for specific mass term interactions.

Contribution

It introduces a detailed classification of four ${ m N}=(4,4)$ twisted supermultiplets within ${ m N}=(2,2)$ superspace and analyzes their sigma model actions and interactions.

Findings

Four types of twisted supermultiplets are described and classified.

Sigma model actions for each type are reduced to separate sums.

Interactions between different types are limited to mass terms within 'self-dual' pairs.

Abstract

We describe four different types of the ${\cal N} = (4,4)$ twisted supermultiplets in two-dimensional ${\cal N} = (2,2)$ superspace ${\bf R}^{1,1|2,2}$. All these multiplets are presented by a pair of chiral and twisted chiral superfields and differ in the transformation properties under an extra hidden ${\cal N} = (2,2)$ supersymmetry. The sigma model ${\cal N} = (2,2)$ superfield Lagrangians for each type of the ${\cal N} = (4,4)$ twisted supermultiplets are real functions subjected to some differential constraints implied by the hidden supersymmetry. We prove that the general sigma model action, with all types of ${\cal N} = (4,4)$ twisted multiplets originally included, is reduced to a sum of sigma model actions for separate types. An interaction between the multiplets of different sorts is possible only through the appropriate mass terms, and only for those multiplets which belong to the same `self-dual' pair.