nLab Brandenberger-Vafa mechanism

Idea

The Brandenberger-Vafa mechanism is an argument, using ingredients of string theory, to deduce that the observable universe is a spacetime of 3+1 large dimensions (in addition to small higher dimensions in a Kaluza-Klein compactification). This is part of the issue of moduli stabilization. One also speaks of “brane gas cosmology”.

The idea is that in the presence of strings and branes, then the winding modes of these objects around cycles of the compactified dimensions (i.e. wrapped branes) induce an energy barrier for compact dimensions to grow large. A more detailed analysis of a “brane gas cosmology” is then argued to yield that exactly 3+1 spactime dimensions may grow large.

A similar claim, with very different methods, is made in (Kim-Nishimura-Tsuchiya 12), via computer simulation of the IKKT matrix model for type IIB string theory.

Related concepts

• cosmology

• moduli stabilization

• landscape of string theory vacua

References

The original article:

• Robert Brandenberger, Cumrun Vafa: Superstrings in the Early Universe, Nucl. Phys. B 316 (1989) 391 [spire263348, doi:10.1016/0550-3213(89)90037-0]

Review:

• Damien A. Easson, section 3 of The Interface of Cosmology with String and M(ILLENNIUM) Theory, Int.J.Mod.Phys.A16:4803-4843,2001 (arXiv:hep-th/0003086)

Further developments:

• Scott Watson, Robert Brandenberger, Stabilization of Extra Dimensions at Tree Level, JCAP 0311 (2003) 008 (arXiv:hep-th/0307044)

• Brian Greene, Daniel Kabat, Stefanos Marnerides, On three dimensions as the preferred dimensionality of space via the Brandenberger-Vafa mechanism, 10.1103/PhysRevD.88.043527 (arXiv:1212.2115)

• Robert Brandenberger, Damien A. Easson, Dagny Kimberly, Loitering Phase in Brane Gas Cosmology, Nucl.Phys. B623 (2002) 421-436 (arXiv:hep-th/0109165)

• Jin Young Kim, Stabilization of the Extra Dimensions in Brane Gas Cosmology with Bulk Flux, Phys.Lett.B652:43-52,2007 (arXiv:hep-th/0608131)

• Brian Greene, Daniel Kabat, Stefanos Marnerides, On three dimensions as the preferred dimensionality of space via the Brandenberger-Vafa mechanism (arXiv:1212.2115)

For a very different argument coming to the same conclusion, within the IKKT matrix model for type IIB string theory, see

• S.-W. Kim, J. Nishimura, and A. Tsuchiya, Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions, Phys. Rev. Lett. 108, 011601 (2012), (arXiv:1108.1540).

• S.-W. Kim, J. Nishimura, and A. Tsuchiya, Late time behaviors of the expanding universe in the IIB matrix model, JHEP 10, 147 (2012), (arXiv:1208.0711).

On relating the Brandenberger-Vafa mechanism to the BFSS matrix model/IKKT matrix model:

• Robert Brandenberger, Julia Pasiecznik: On the Origin of the $SO(9) \to SO(3) \times SO(6)$ Symmetry Breaking in the IKKT Matrix Model [arXiv:2409.00254]

• Robert Brandenberger: Emergent Metric Space-Time from the BFSS Matrix Model, talk at Perimeter Institute (May 2023) [doi:10.48660/23050109, video:pirsa:23050109, slides:pdf]