Matrix model and Yukawa couplings on the noncommutative torus

J. Dixmier, “Représentations irrèducibles des algèbrs de Lie nilpotentes”, An. Acad. Brasil. Ci 𝟑𝟓 {\bf 35} (1963) 491-519

1963

Earlier work this paper cites.

D. Quillen, “On the endomorphism ring of a simple module over an enveloping algebra” Proc. Amer. Math. Soc. 𝟐𝟏 {\bf 21} (1969) 171-172

1969

Earlier work this paper cites.

D. Mumford, Tata lectures on theta I

1983

Earlier work this paper cites.

M. A. Rieffel, “Projective modules over higher-dimensional non-commutative tori”, Can. J. Math. Vol. 𝐗𝐋 {\bf XL} No.2 (1988) 257-338

1988

Earlier work this paper cites.

N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, “A Large N reduced model as superstring,” Nucl. Phys. B 498

1997

Earlier work this paper cites.

A. Connes, M. R. Douglas and A. S. Schwarz, “Noncommutative geometry and matrix theory: Compactification on tori,” JHEP 9802

1998

Earlier work this paper cites.

N. Seiberg and E. Witten, “String theory and noncommutative geometry,” JHEP 9909

1999

Earlier work this paper cites.

A. Konechny and A. S. Schwarz, “Compactification of M(atrix) theory on noncommutative toroidal orbifolds,” Nucl. Phys. B 591

2000

Earlier work this paper cites.

P. Austing and J. F. Wheater, “The Convergence of Yang-Mills integrals,” JHEP 0102

2001

Cited alongside, same era.

P. Austing and J. F. Wheater, “Convergent Yang-Mills matrix theories,” JHEP 0104

2001

Cited alongside, same era.

A. Konechny and A. S. Schwarz, “Introduction to M(atrix) theory and noncommutative geometry,” Phys. Rept. 360

2002

Cited alongside, same era.

D. Cremades, L. E. Ibáñez and F. Marchesano, “Computing Yukawa couplings from magnetized extra dimensions,” JHEP 0405

2004

Cited alongside, same era.

Y. Tenjinbayashi, H. Igarashi and T. Fujiwara, “Dirac operator zero-modes on a torus,” Annals Phys. 322

2007

Cited alongside, same era.

H. Steinacker, “Emergent Gravity from Noncommutative Gauge Theory,” JHEP 0712

J. Nishimura and A. Tsuchiya, “Realizing chiral fermions in the type IIB matrix model at finite N,” JHEP 1312

Original

2013

Later among the works it cites.

H. Abe, T. Kobayashi, H. Ohki, A. Oikawa and K. Sumita, “Phenomenological aspects of 10D SYM theory with magnetized extra dimensions,” Nucl. Phys. B 870

Original

2013

Later among the works it cites.

H. Aoki, J. Nishimura and A. Tsuchiya, “Realizing three generations of the Standard Model fermions in the type IIB matrix model,” JHEP 1405

Original

2014

Later among the works it cites.

S. Walters, “Toroidal orbifolds of ℤ 3 \mathbb{Z}_{3} and ℤ 6 \mathbb{Z}_{6} symmetries of noncommutative tori,” Nucl. Phys. B 894

2015

Later among the works it cites.

T. Asakawa and S. Matsuura, “Spherical D-brane by Tachyon Condensation,” PTEP 2018