Metric-Independent Measures for Supersymmetric Extended Object Theories on Curved Backgrounds

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For Green-Schwarz superstring sigma-model on curved backgrounds, we introduce a non-metric measure Φ≡ εⁱ ʲ εⁱ ʲ (∂ᵢ φⁱ) (∂ⱼ φʲ) with two scalars φⁱ (I = 1, 2) used in Two Measure Theory (TMT). As in the flat-background case, the string tension T= (2 πα')⁻¹ emerges as an integration constant for the Aᵢ-field equation. This mechanism is further generalized to supermembrane theory, and to super p-brane theory, both on general curved backgrounds. This shows the universal applications of dynamical measure of TMT to general supersymmetric extended objects on general curved backgrounds.