Form Factors of Exponential Operators and Exact Wave Function Renormalization Constant in the Bullough-Dodd Model

TL;DR

This paper calculates exact form factors and the wave-function renormalization constant for exponential operators in the integrable Bullough-Dodd model, linking to minimal models and providing precise operator data.

Contribution

It provides explicit form factors for exponential operators and the exact wave-function renormalization constant in the Bullough-Dodd model, extending understanding of operator structure in integrable quantum field theories.

Findings

Explicit form factors for exponential operators computed.

Wave-function renormalization constant Z(g) obtained exactly.

Form factors of primary fields in related minimal models derived.

Abstract

We compute the form factors of exponential operators $e^{kg\varphi(x)}$ in the two-dimensional integrable Bullough-Dodd model ($a_2^{(2)}$ Affine Toda Field Theory). These form factors are selected among the solutions of general nonderivative scalar operators by their asymptotic cluster property. Through analitical continuation to complex values of the coupling constant these solutions permit to compute the form factors of scaling relevant primary fields in the lightest-breather sector of integrable $\phi_{1,2}$ and $\phi_{1,5}$ deformations of conformal minimal models. We also obtain the exact wave-function renormalization constant Z(g) of the model and the properly normalized form factors of the operators $\varphi(x)$ and $:\varphi^2(x):$.