Gauge five-brane moduli in four-dimensional heterotic models

We present a Kähler 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 Kähler 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