Open/Closed Topological CP1 Sigma Model Revisited

TL;DR

This paper revisits the topological CP1 sigma model on Riemann surfaces, analyzing correlation functions, symmetries, deformations, and the open/closed TFT correspondence, including coupling to topological gravity.

Contribution

It provides a comprehensive analysis of the open/closed topological CP1 sigma model, including correlation functions, symmetries, deformations, and the impact of summing boundaries as a form of renormalization.

Findings

Correlation functions of bulk and boundary operators calculated.

Open/closed TFT correspondence established through boundary summation.

Coupling to topological gravity yields new relations between correlators.

Abstract

We consider the topological sigma-model on Riemann surfaces with genus g and h holes, and target space CP1. We calculate the correlation functions of bulk and boundary operators, and study the symmetries of the model and its most general deformation. We study the open/closed topological field theory (TFT) correspondence by summing up the boundaries. We argue that this summation can be understood as a renormalization of the closed TFT. We couple the model to topological gravity and derive constitutive relations between the correlation functions of bulk and boundary operators.