The 3+1-dimensional Einstein-Hilbert action is obtained from the 1-loop effective action on noncommutative branes in the IIB or IKKT matrix model. The presence of compact fuzzy extra dimensions K as well as maximal supersymmetry of the model is essential. The E-H action can be interpreted as interaction of K with the space-time brane via IIB supergravity, and the effective Newton constant is determined by the Kaluza-Klein scale of K. The classical matrix model defines a pre-gravity action with 2 derivatives less than the induced E-H action, governing the cosmological regime. The perturbative physics is confined to the space-time brane, which for covariant quantum space-times includes all dof of gravity, as well as a tower of higher-spin modes. The vacuum energy of the background is given in terms of the symplectic volume form, and hence does not act as cosmological constant.
Physics Letters B
- Pub Date:
- April 2022
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- 6 pages. V2: dilaton contribution corrected, references added, published version