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2011

Fuzzy spaces and new random matrix ensembles

Nair, V. P., Polychronakos, A. P., Tekel, J.

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We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model.

We calculate explicitly the form of the expectation values in the large-N limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius.
For observables involving more than one type of matrix we obtain a new distribution corresponding to correlated Wigner semicircles.

Fuzzy spaces and new random matrix ensembles · Around

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For a review of the matrix version of M-theory and its solutions, see, W. Taylor IV, Rev. Mod. Phys. 73
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For a review of field theories on noncommutative spaces, see, M.R. Douglas and N.A. Nekrasov, Rev. Mod. Phys. 73
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Earlier work this paper cites.

Similar

H. Steinacker, Nucl. Phys. B 679
2005
Cited alongside, same era.
L. Susskind, hep-th/0101029; A. P. Polychronakos, JHEP 0104
2005
Cited alongside, same era.
For reviews with applications to Calogero systems and other condensed matter examples, see T. Guhr, A. Müller-Groeling and H.A. Weidenmüller, Phys. Rep. 299
2006
Cited alongside, same era.

Then

D. Voiculescu, J. Funct. Anal., 66
2006
Later among the works it cites.
D. O’Connor, C. Saemann, JHEP 0708
2007
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M.V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 356
2010
Later among the works it cites.

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