Born-Infeld Action and Chern-Simons Term from Kaluza-Klein Monopole in M-theory
Yosuke Imamura
TL;DR
The work demonstrates that the D6-brane worldvolume action, comprising $S_{ m BI}$ and $S_{ m CS}$, can be derived from the zero modes of a Kaluza-Klein monopole in M-theory, up to quadratic order in the worldvolume field strength $V_{ij}$. By analyzing Taub-NUT geometry and performing a careful KK reduction, the authors identify $(L,N)=(0,0)$ zero modes for the $U(1)$ gauge field and the NS-NS 2-form, fix their normalizations to match the 10D NS-NS kinetic term and RR couplings, and reproduce the $V_{ij}^2$ term as well as the first three Chern-Simons contributions. Key technical steps include solving the mode equations on Taub-NUT, enforcing anti-self-duality for normalizable $A_{\mu u}$, and relating $A_{ m ijk}$ to the RR 3-form $C_{ijk}$; explicit normalization constants are obtained (e.g., $c_2=- rac{1}{(2\
Abstract
We investigate the zero modes of the Kaluza-Klein monopole in M-theory and show that the Born-Infeld action and the Chern-Simons term of a D6-brane are reproduced to quadratic order in the field strength of the U(1) field on the brane.