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IKKT matrix model

Contents

Contents

Idea

The KK-compactification of D=10 super Yang-Mills theory all the way to the point yields a theory whose fields are simply elements of the gauge Lie algebra 𝔤\mathfrak{g}, hence matrices for a matrix Lie algebra. This physics is called the IKKT matrix model.

Alternatively this model can be motivated from a certain regularization of the worldsheet action functional of the superstring. This is how it was originally obtained in (IKKT 96).

It has been argued that for 𝔤=𝔰𝔲(N)\mathfrak{g} = \mathfrak{su}(N) for large NN, this model captures aspects of non-perturbative type IIB string theory (see also at M-theory). Therefore this is also called the IIB matrix model (in contast to the BFSS matrix model in type IIA string theory).

Several authors have explored the possibility to lift the derivation of the IKKT model from the superstring to the M2-brane. See at membrane matrix model for more on this.

In (Kim-Nishimura-Tsuchiya 12) it is claimed that computer simulation of the IKKT matrix model, regarded as non-perturbative type IIB string theory, shows a spontaneous emerging spacetime of macroscopic dimension 3+1, with 6 microscopic dimensions. (A similar claim results from a very different argument: the Brandenberger-Vafa mechanism.)

References

General

The original articles are

  • N. Ishibashi, H. Kawai, Y. Kitazawa, A. Tsuchiya, A Large-N Reduced Model as Superstring, Nucl.Phys. B498 (1997) 467-491 (arXiv:hep-th/9612115)

  • H. Aoki, S. Iso, H. Kawai, Y. Kitazawa, T. Tada, A. Tsuchiya, IIB Matrix Model, Prog.Theor.Phys.Suppl.134:47-83,1999 (arXiv:hep-th/9908038)

See also

Derivation from open string field theory is discussed in

Arguments that full Yang-Mills theory generalized to noncommutative geometry is recovered as the perturbation theory around classical solutions of the IKKT model are in

  • H. Aoki, N. Ishibashi, S. Iso, H. Kawai, Y. Kitazawa, T. Tada, Noncommutative Yang-Mills in IIB Matrix Model, Nucl.Phys. B565 (2000) 176-192 (arXiv:hep-th/9908141)

  • Tatsuo Azeyanagi, Masanori Hanada, Tomoyoshi Hirata, On Matrix Model Formulations of Noncommutative Yang-Mills Theories, Phys.Rev.D78:105017,2008 (arXiv:0806.3252)

Arguments that closed string field theory arises from the dynamics of Wilson loops IKKT model are in

  • M. Fukuma, H. Kawai, Y. Kitazawa, A. Tsuchiya, String Field Theory from IIB Matrix Model, Nucl.Phys.B510:158-174,1998 (arXiv:hep-th/9705128)

  • Daiji Ennyu, Hiroshi Kawabe, Naohito Nakazawa, Note on a Closed String Field Theory from Bosonic IIB Matrix Model, JHEP 0301 (2003) 025 (arXiv:hep-th/0212044)

Possibilities of generalizing the IKKT model from Lie algebras to Lie 2-algebras in some membrane matrix model are explored in

Discussion of standard model phenomenology within the IKKT model includes

See also

  • A. Stern, Chuang Xu, Signature change in matrix model solutions (arXiv:1808.07963)

Computer simulation

There are claims that numerical computer simulations (as in lattice gauge theory, see the references there) show that the IKKT matrix model predicts a spontanously generated spacetime where exactly 3+1 dimensions become macroscopic (hence effectively predicts moduli stabilization in spintaneous KK-compactification of M-theory to D=3+1D = 3+1 macroscopic dimensions ):

  • 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).

  • Yuta Ito, Jun Nishimura, Asato Tsuchiya, Large-scale computation of the exponentially expanding universe in a simplified Lorentzian type IIB matrix model (arXiv:1512.01923)

  • Toshihiro Aoki, Mitsuaki Hirasawa, Yuta Ito, Jun Nishimura, Asato Tsuchiya, On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model (arXiv:1904.05914)

Last revised on July 23, 2019 at 15:46:10. See the history of this page for a list of all contributions to it.