Matrix Models and Geometry of Moduli Spaces
| dc.creator | Chekhov, L. | |
| dc.date | 1995-09-01 | |
| dc.date.accessioned | 2026-07-07T09:14:29Z | |
| dc.date.available | 2026-07-07T09:14:29Z | |
| dc.description | We give the description of discretized moduli spaces (d.m.s.) $\Mcdisc$ introduced in \cite{Ch1} in terms of discrete de Rham cohomologies for moduli spaces $\Mgn$. The generating function for intersection indices (cohomological classes) of d.m.s. is found. Classes of highest degree coincide with the ones for the continuum moduli space $\Mc$. To show it we use a matrix model technique. The Kontsevich matrix model is the generating function in the continuum case, and the matrix model with the potential $Nα\tr {\bigl(- \fr 14 ŁXŁX -\fr12\log (1-X)-\fr12X\bigr)}$ is the one for d.m.s. In the latest case the effects of Deligne--Mumford reductions become relevant, and we use the stratification procedure in order to express integrals over open spaces $\Mdisc$ in terms of intersection indices, which are to be calculated on compactified spaces $\Mcdisc$. We find and solve constraint equations on partition function $\cal Z$ of our matrix model expressed in times for d.m.s.: $t^\pm_m=\tr \fr{\d^m}{\dł^m}\fr1{\e^ł-1}$. It appears that $\cal Z$ depends only on even times and ${\cal Z}[t^\pm_\cdot]=C(åN) \e^{\cal A}\e^{F(\{t^{-}_{2n}\}) +F(\{-t^{+}_{2n}\})}$, where $F(\{t^\pm_{2n}\})$ is a logarithm of the partition function of the Kontsevich model, $\cal A$ being a quadratic differential operator in $\dd{t^\pm_{2n}}$. | |
| dc.description | 40pp., LaTeX, no macros needed, 8 figures in text | |
| dc.identifier | https://arxiv.org/abs/hep-th/9509001 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9509001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152691 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Matrix Models and Geometry of Moduli Spaces | |
| dc.type | text |