Coupling Constants and Brane Tensions from Anomaly Cancellation in M-theory

TL;DR

This paper investigates anomaly cancellation in M-theory on R^10 x S^1/Z_2, deriving relations between coupling constants, brane tensions, and flux quantization, clarifying gauge invariance issues and boundary conditions.

Contribution

It provides a detailed analysis of anomaly cancellation, boundary conditions, and flux quantization in M-theory, establishing relations between coupling constants and brane tensions.

Findings

Unique boundary value of four-form field strength

Relation between eleven-dimensional coupling constants

Standard form of brane tensions in 'downstairs' units

Abstract

The theory of eleven dimensional supergravity on R^10 x S^1/Z_2 with super Yang-Mills theory on the boundaries is reconsidered. We analyse the general solution of the modified Bianchi identity for the four-form field strength using the equations of motion for the three-form and find that the four-form field strength has a unique value on the boundaries of R^10 x S^1/Z_2. Considering the local supersymmetry in the "downstairs" approach this leads to a relation between the eleven dimensional supergravity coupling constants in the "upstairs" and "downstairs" approaches. Moreover, it is shown using flux quantization that the brane tensions only have their standard form in the "downstairs" units. We consider the gauge variation of the classical theory and find that it cannot be gauge invariant, contrary to a recent claim. Finally we consider anomaly cancellation in the "downstairs" and "upstairs" approaches and obtain the values of lambda^6/kappa^4 and the two- and five-brane tensions.