Instantons beyond topological theory I

TL;DR

This paper explores quantum field theories with instantons in specific limits, revealing exact spectra, logarithmic behaviors, and holomorphic structures, thus extending understanding beyond topological sectors.

Contribution

It provides a detailed analysis of instanton effects beyond topological sectors, showing exact correlation functions, spectrum, and the emergence of logarithmic conformal field theories.

Findings

Correlation functions can be explicitly computed for all observables.

The spectrum may include Jordan blocks, leading to logarithms.

Models on Kahler manifolds exhibit holomorphic factorization.

Abstract

Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kahler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories.