Form factors in the presence of integrable defects

Abstract

Form factor axioms are derived in two dimensional integrable defect theories for matrix elements of operators localized both in the bulk and on the defect. The form factors of bulk operators are expressed in terms of the bulk form factors and the transmission factor. The structure of the form factors of defect operators is established in general, and explicitly calculated in particular, for the free boson and for some operator of the Lee-Yang model. Fusion method is also presented to generate boundary form factor solutions for a fused boundary from the known unfused ones.Comment: 21 pages, 13 eps figure

Entanglement entropy in integrable field theories with line defects. Part I. Topological defect

“…This confirms our claim that we can move topological defects freely within the interval. The same result can also be obtained from a slightly different point of view from the defect form factor axioms [18].…”

“…In the presence of a line defect, if the local operator does not sit on the defect, the form factor of the operator are essentially the same as the bulk case [18]. On the other hand, the presence of the defect affects the spectral expansion of correlation functions and gives rise to extra factors which are matrix elements of the defect operator.…”

“…In this section, we review line defects in integrable field theories. Our discussion mainly follows the seminal papers [16,17] and [18,40].…”

“…In general, these additional structures will spoil the integrability of the theory. However, there exist special kinds of boundaries and defects that preserve integrability [15][16][17][18] which allow one to apply powerful integrability techniques. In [10], the authors investigated Ising model with integrable boundary conditions.…”

“…This question has been investigated extensively for spin models and conformal field theories, see for example [19][20][21][22][23][24][25] and references therein. Secondly, defects often contain useful information about the structure of the bulk theory and thus classification and the study of the defects are of considerable theoretical interest [18,[26][27][28][29][30][31][32][33][34].…”