Abstract
We apply the renormalized coupling constants and Virasoro constraints to derive the Itzykson-Zuber Ansatz on the form of the free energy in 2D topological gravity. We also treat the 1D topological gravity and the Hermitian one-matrix models in the same fashion. Some uniform behaviors are discovered in this approach.
Highlights
In recent years there have appeared various Gromov-Witten type theories. In all these theories we study their partition functions or free energy functions, expressed as formal power series in infinitely many formal variables
Similar to the case of 1D topological gravity, we rewrite the Virasoro constraints for Hermitian one-matrix models in I-coordinates and use them to derive the explicit formulas for the free energy in Icoordinates
We have developed the techniques of rewriting all the Virasoro constraints for free energies in I-coordinates and solving free energies recursively
Summary
In recent years there have appeared various Gromov-Witten type theories. In all these theories we study their partition functions or free energy functions, expressed as formal power series in infinitely many formal variables. The proofs of (1.15) and (1.16) in previous works of the second named author are based on rewriting the corresponding puncture equation and the dilaton equation in 1D topological gravity and Hermitian one-matrix models in terms of the I-coordinates. It was announced in [28] that the same method can be applied to establish the Itzykson-Zuber ansatz. In [33] the second named author introduced some coupling constants t−n for n ≥ 1 and call them the ghost variables They were used to defined the following extension of free energy F02D in genus zero: F02D = F02D + (−1)n(tn − δn,1)t−n−1. We study the special deformation of the 1D gravity in I-coordinates
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
