Abstract
We review matrix models corresponding to triangulations of the moduli space of Riemann surfaces: primarily the Kontsevich model that computes intersection numbers on moduli space, and the Penner model that computes the virtual Euler characteristic of moduli space. Generalisations of the former model describe noncritical strings with c < 1 matter, while the latter can be generalised to describe amplitudes of c = 1 strings at selfdual radius.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. A. Kazakov, A. A. Migdal and I. K. Kostov, “Critical Properties Of Randomly Triangulated Planar Random Surfaces”, Phys. Lett. B 157(1985) 295.
E. Brezin and V. A. Kazakov, “Exactly Solvable Field Theories Of Closed Strings”, Phys. Lett. B 236(1990) 144.
M. R. Douglas and S. H. Shenker, “Strings In Less Than One-Dimension”, Nucl. Phys. B 335(1990) 635.
D. J. Gross and A. A. Migdal, “Nonperturbative Two-Dimensional Quantum Gravity”, Phys. Rev. Lett. 64(1990) 127.
T. Takayanagi and N. Toumbas, “A matrix model dual of type 0B string theory in two dimensions”, JHEP 0307(2003) 064 [arXiv:hep-th/0307083].
M. R. Douglas, I. R. Klebanov, D. Kutasov, J. Maldacena, E. Martinec and N. Seiberg, “A new hat for the c = 1 matrix model”, arXiv:hep-th/0307195.
M. Kontsevich, “Intersection theory on the moduli space of curves and the matrix Airy function”, Commun. Math. Phys. 147(1992) 1.
R. Penner, “Perturbative series and the moduli space of Riemann surfaces”, J. Diff. Geom. 27(1988) 35.
E. Witten, “On the structure of the topological phase of two-dimensional gravity”, Nucl. Phys. B 340(1990) 281.
J. Distler and C. Vafa, “A critical matrix model at c = 1”, Mod. Phys. Lett. A 6(1991) 259.
J. McGreevy and H. Verlinde, “Strings from tachyons: The c = 1 matrix reloaded”, arXiv:hep-th/0304224.
I. R. Klebanov, J. Maldacena and N. Seiberg, “D-brane decay in two-dimensional string theory”, JHEP 0307(2003) 045 [arXiv:hep-th/0305159].
D. Gaiotto and L. Rastelli, “A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model”, arXiv:hep-th/0312196.
V. Fateev, A. B. Zamolodchikov and A. B. Zamolodchikov, “Boundary Liouville .eld theory. I: Boundary state and boundary two-point function”, arXiv:hep-th/0001012.
J. Teschner, “Remarks on Liouville theory with boundary”, arXiv:hep-th/0009138.
A. B. Zamolodchikov and A. B. Zamolodchikov, “Liouville .eld theory on a pseudosphere”, arXiv:hep-th/0101152.
J. L. Harer and D. Zagier, “The Euler characteristic of the moduli space of curves”, Inv. Math. 85(1986) 457.
J. L. Harer, “The cohomology of the moduli space of curves”, in “Theory of Moduli”, Lecture Notes in Mathematics, Springer-Verlag (1988), E. Sernesi (Ed.).
K. Strebel, “Quadratic Differentials”, Springer-Verlag (1984).
S. Mukhi, “Topological matrix models, Liouville matrix model and c = 1 string theory”, arXiv:hep-th/0310287.
D. Mumford, “Towards An Enumerative Geometry Of The Moduli Space Of Curves,” in Arithmetic And Geometry, eds. M. Artin and J. Tate (Birkhauser, 1985).
S. Morita, “Characteristic Classes of Surface Bundles,” Invent. Math. 90(1987) 551.
E. Miller, “The Homology Of The Mapping Class Group,” J. Diff. Geom. 24(1986) 1.
E. Witten, “Two-Dimensional Gravity And Intersection Theory On Moduli Space”, Surveys Diff. Geom. 1(1991) 243.
E. Witten, “On the Kontsevich model and other models of two-dimensional gravity”, IASSNS-HEP-91–24
M. Adler and P. van Moerbeke, “A Matrix integral solution to two-dimensional W(p) gravity" Commun. Math. Phys. 147(1992) 25.
S. Kharchev, A. Marshakov, A.Mironov, A. Morozov and A. Zabrodin, “Towards uni.ed theory of 2-d gravity”, Nucl. Phys. B 380(1992) 181 [arXiv:hep-th/9201013].
I. R. Klebanov, “String theory in two dimensions”, arXiv:hep-th/9108019.
C. Imbimbo and S. Mukhi, “The topological matrix model of c = 1 string”, Nucl. Phys. B 449(1995) 553 [arXiv:hep-th/9505127].
R. Dijkgraaf, G. W. Moore and R. Plesser, “The partition function of 2-D string theory”, Nucl. Phys. B 394(1993) 356 [arXiv:hep-th/9208031].
S. Y. Alexandrov, V. A. Kazakov and I. K. Kostov, "2-D string theory as normal matrix model”, Nucl. Phys. B 667(2003) 90 [arXiv:hep-th/0302106].
D. Ghoshal, S. Mukhi and S. Murthy, “Liouville D-branes in two-dimensional strings and open string .eld theory”, JHEP 0411(2004) 027 [arXiv:hep-th/0406106].
R. Dijkgraaf and C. Vafa, “N = 1 supersymmetry, deconstruction, and bosonic gauge theories”, arXiv:hep-th/0302011.
M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino and C. Vafa, “Topological strings and integrable hierarchies”, arXiv:hep-th/0312085.
M. Aganagic, H. Ooguri, N. Saulina and C. Vafa, “Black holes, q-deformed 2d Yang- Mills, and non-perturbative topological strings”, arXiv:hep-th/0411280.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Mukhi, S. (2006). MATRIX MODELS OF MODULI SPACE. In: Brézin, É., Kazakov, V., Serban, D., Wiegmann, P., Zabrodin, A. (eds) Applications of Random Matrices in Physics. NATO Science Series II: Mathematics, Physics and Chemistry, vol 221. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4531-X_10
Download citation
DOI: https://doi.org/10.1007/1-4020-4531-X_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4529-5
Online ISBN: 978-1-4020-4531-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)