Topological-Antitopological Fusion and the Large N CP^N Model

Abstract

We discuss the large $N$ limit of the supersymmetric $C{P}^N$ models as an illustration of Cecotti and Vafa's $t{t}^{\ast }$ formalism. In this limit the `$t{t}^{\ast }$ equation' becomes the long wavelength limit of the $2D$ Toda lattice, an equation first studied in the context of self-dual gravity. We show how simple finite temperature and large $N$ techniques determine the relevant solution, and verify analytically that it solves the $t{t}^{\ast }$ equation, using Legendre transform techniques from self-dual gravity.

24 pages (LaTeX), OUTP-93-24P and RU-93-56

References in corpus (3)

• A New Supersymmetric Index
• Exact Results for Supersymmetric Sigma Models
• N=2 Supersymmetry, Painleve III and Exact Scaling Functions in 2D Polymers

Cited by in corpus (3)

• The Exact Mass-Gap of the Supersymmetric CP^{n-1} Sigam Model
• Grassmannian Sigma Models and Topological-Antitopological Fusion
• Supersymmetric Sigma Models on Toric Varieties: A Test Case