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 4dimensional 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 ) 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 × AdS 5 bulk geometry around a stack of branes. SUSY may be broken by compact extra dimensions , leading to an induced gravitational action on 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.