S Matrices of the Tricritical Ising Model and Toda Systems

Abstract

After the excellent discussion of the subject presented at this conference by E. Corrigan, it would be redundant to repeat in detail the different steps that make it possible to simplify the difficult problem of the determination of the S matrices in certain integrable off-critical systems. Instead, I will only briefly review the different tools, those developed by Zamolod-chikov [1], and the arguments that connect the subject to Toda field theories [2, 3, 4], in an effort to add new comments about each of them. The Tricritical Ising Model (TIM), that will be the standard example, is discussed in more detail in ref.[5], written with G. Mussardo. The interesting examples of the D n Toda systems are discussed in [6] and in the talk of E. Corrigan at this conference. In a second part, I will discuss in more detail certain selected features of Toda systems. The rich multipole structure and the connection of the exact solution for the S functions to the perturbative expansion is discussed. Finally I will comment on the relation between unitary and non-unitary off-critical integrable models that seems very closely related. The content of this talk represents the results obtained in collaboration with Giuseppe Mussardo.