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

TL;DR

This paper introduces a metric-independent measure in supersymmetric extended object theories on curved backgrounds, allowing string tension to emerge dynamically as an integration constant, with applications to supermembranes and p-branes.

Contribution

It generalizes the Two Measure Theory to supersymmetric extended objects on curved backgrounds, demonstrating a universal mechanism for dynamical tension emergence.

Findings

String tension arises as an integration constant.

The measure is applicable to supermembranes and p-branes.

Universal application of TMT to curved supersymmetric backgrounds.

Abstract

For Green-Schwarz superstring sigma-model on curved backgrounds, we introduce a non-metric measure $\Phi \equiv \epsilon^{i j} \epsilon^{I J} (\partial_i \varphi^I) (\partial_j \varphi^J)$ with two scalars $\varphi^I (I = 1, 2)$ used in Two Measure Theory (TMT). As in the flat-background case, the string tension $T= (2 \pi \alpha ' )^{-1}$ emerges as an integration constant for the A_i-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.