On the 1-loop effective action for the IKKT model and non-commutative branes

We study the one-loop effective action of the IKKT or IIB model on a 4-dimensional non-commutative brane background. The trace-U(1) sector is governed by non-commutativity, and leads - assuming no SUSY breaking - to a higher-derivative effective action. In contrast, the non-Abelian sector at low energies reduces to SU(n) N=4 Super-Yang-Mills on the brane, with a global SO(9,1) symmetry broken spontaneously by the background. In the Coulomb branch, we recover the leading contribution to the Dirac-Born-Infeld (DBI) action, exhibiting a S^5 \times AdS^5 bulk geometry around a stack of branes. SUSY may be broken by compact extra dimensions M^4 x K, leading to an induced gravitational action on M^4 due to the trace-U(1) sector. The one-loop effective action is UV finite on such backgrounds, and the UV/IR mixing is non-pathological.