Metric-independent measures for supersymmetric extended object theories on curved backgrounds

For Green–Schwarz superstring σ  -model on curved backgrounds, we introduce a non-metric measure Φ≡ϵijϵIJ(∂iφI)(∂jφJ)Φ≡ϵijϵIJ(∂iφI)(∂jφJ) with two scalars φI(I=1,2) used in ‘Two-Measure Theory’ (TMT). As in the flat-background case, the string tension T=(2πα′)−1T=(2πα′)−1 emerges as an integration constant for the AiAi-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.