Anomaly Cancellation in Seven-Dimensional Supergravity with a Boundary

TL;DR

This paper constructs a seven-dimensional brane world model with anomaly cancellation conditions fixing boundary gauge couplings, revealing restrictions on gauge groups and potential phase transitions, and explores its duality with six-dimensional conformal field theories.

Contribution

It provides a consistent supersymmetric brane world setup in seven dimensions with anomaly cancellation, linking boundary gauge groups to exceptional groups and analyzing phase transition points.

Findings

Anomaly cancellation fixes boundary gauge couplings.

Boundary gauge groups restricted to exceptional groups.

Potential phase transition at specific boundary separations.

Abstract

We construct a seven-dimensional brane world in a slice of AdS_7, where the boundary matter content is fixed by the cancellation of anomalies. The seven-dimensional minimal N=2 gauged supergravity is compactified on the orbifold S^1/Z_2, and the supersymmetric bulk-boundary Lagrangian is consistently derived for boundary vector and hypermultipets up to fermionic bilinear terms. Anomaly cancellation then fixes the boundary gauge coupling in terms of the seven-dimensional Planck mass, and a topological mass parameter of the Chern-Simons term. In addition for gauge groups containing the standard model, anomaly cancellation restricts the gauge groups on the six-dimensional boundaries to be only one of the exceptional groups. There are also special values of the separation of the two boundaries, where the boundary couplings become singular, and lead to a possible phase transition in the boundary theory. Furthermore, by the AdS/CFT correspondence our brane world is dual to a six-dimensional conformal field theory, suggesting that our bulk theory describes the strong coupling dynamics of six-dimensional theories.