Topological Correlation Functions in Minkowski Spacetime

TL;DR

This paper explores topological correlation functions in a twisted, non-unitary Toda theory based on Lie superalgebras in Minkowski spacetime, revealing integrable structures and chiral rings using superspace methods.

Contribution

It introduces a novel approach to compute topological correlation functions in a twisted non-unitary Toda theory with Lie superalgebra symmetry.

Findings

Constructed conserved currents and vertex operators.

Defined the chiral ring of the $A^{(1)}(1,1)$ Toda theory.

Computed topological correlation functions using superspace techniques.

Abstract

We consider a class of non-unitary Toda theories based on the Lie superalgebras $A^{(1)}(n,n)$ in two-dimensional Minkowski spacetime, which can be twisted into a topological sector. In particular we study the simplest example with $n=1$ and real fields, and show how this theory can be treated as an integrable perturbation of the $A(1,0)$ superconformal model. We construct the conserved currents and the vertex operators which are chiral primary fields in the conformal theory. We then define the chiral ring of the $A^{(1)}(1,1)$ Toda theory and compute topological correlation functions in the twisted sector. The calculation is performed using a $N=2$ off--shell superspace approach.