Brane Tensions and Coupling Constants from within M-Theory

TL;DR

This paper rederives the Yang-Mills coupling constant in M-theory on R^10 x S^1/Z_2, showing its consistency with brane tensions and proposing natural units where these tensions and couplings take standard forms.

Contribution

It provides a corrected calculation of the Yang-Mills coupling constant in M-theory and clarifies the appropriate units for describing brane tensions and couplings.

Findings

Derived the Yang-Mills coupling constant consistent with M-theory anomaly cancellation.

Showed compatibility of coupling constants with membrane and fivebrane tensions.

Proposed natural units where brane tensions and couplings are in standard form.

Abstract

Reviewing the cancellation of local anomalies of M-theory on R^10 x S^1/Z_2 the Yang-Mills coupling constant on the boundaries is rederived. The result is lambda^2 = 2^(1/3) (2 pi) (4 pi kappa^2)^(2/3) corresponding to eta = lambda^6/kappa^4 = 256 pi^5 in the `upstairs' units used by Horava and Witten and differs from their calculation. It is shown that these values are compatible with the standard membrane and fivebrane tensions derived from the M-theory bulk action. In view of these results it is argued that the natural units for M-theory on R^10 x S^1/Z_2 are the `downstairs' units where the brane tensions take their standard form and the Yang-Mills coupling constant is lambda^2 = 4 pi (4 pi kappa^2)^(2/3).