Gauge Five Brane Moduli In Four-Dimensional Heterotic Models

TL;DR

This work derives a four-dimensional effective action for heterotic M-theory that explicitly includes the moduli of a gauge five brane, realized as a wrapped instanton on a Calabi–Yau fixed plane. By constructing a local approximate background near the brane and promoting integration constants to 4D fields with compensators, the authors obtain a Kahler potential that encompasses the gauge bundle moduli alongside the standard dilaton and Kähler moduli, yielding a consistent N=1 supersymmetric moduli space. The results show how the instanton moduli couple nontrivially to geometric moduli, confirm the Kahler structure, and provide a tractable truncation to simpler two-field models, enabling exploration of brane cosmology and gauge bundle dynamics in four dimensions. The approach avoids requiring a full global background solution and clarifies when gauge bundle moduli cannot be consistently truncated, with potential applications to cosmological scenarios and brane collisions in string theory compactifications.

Abstract

We present a Kahler potential for four dimensional heterotic M-theory which includes moduli describing a gauge five brane living on one of the orbifold fixed planes. This result can also be thought of as describing compactifications of either of the weakly coupled heterotic strings in the presence of a gauge five brane. This is the first example of a Kahler potential in these theories which includes moduli describing background gauge field configurations. Our results are valid when the solitons width is much smaller than the size scale of the Calabi-Yau threefold and can be used to provide a more complete description of some moving brane scenarios. We point out that, in general, it is not consistent to truncate away the gauge five brane moduli in a simple manner.