Abstract
We present the N = 4 superspace constraints for the two-dimensional off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I, as well as the corresponding component results, in a form suitable for applications. The constraints are shown to be invariant under the N = 4 super-Weyl transformations, whose N = 4 superfield parameters form another twisted (scalar) multiplet TM-II. To solve the constraints, we propose an ansatz which makes the N = 4 superconformal flatness of the N = 4 supergravity curved superspace manifest. Locally (4,4) supersymmetric TM-I matter couplings are constructed, with potential terms resulting from spontaneous supersymmetry breaking. We also find the full (4,4) superconformally invariant (improved) TM-II matter action. The latter can be extended to the (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.
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