Asymptotic factorisation of form factors in two-dimensional quantum field theory

Abstract

It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the form factor bootstrap approach. A sum rule which yields the scaling dimension of such operators is also derived.

Matrix elements of the operator in integrable quantum field theory

“…Relying on the arguments of [15] we expect that these factorization conditions actually hold for any operator L lLl Φ 0 in the Lee-Yang model. This requires in particular that the solution for TT factorizes as…”

“…Since the l.h.s. of (4.9) is in fact a limit into the conformal point [15], these subleading terms depend on the way the composite operator TT is defined away from criticality.…”

“…It was argued in [15] that the absence of interaction between right-and left-moving particles at high energies in 1+1 dimensions is at the origin of a factorization of form factors when a subset of momenta becomes asymptotically large. Being non-linear in the operators the factorization equations single out specific solutions within the linear subspaces selected by the asymptotic bound and have been exploited for the identification of primary operators, in particular in the above mentioned case of the Ising model in a magnetic field [13,14].…”

“…We first require an upper bound on the asymptotic behavior and show that it indeed leads to a subspace of solutions with the expected dimensionality. Then we impose an asymptotic factorization condition which is a generalization of that discussed in [15] and identifies the operator TT up to terms which are subleading in the massless limit. Finally, these subleading terms are fixed exploiting the conditions on the expectation values of TT recently derived in [16].…”

First-order phase transitions and integrable field theory. The dilute q-state Potts model

“…The spectral series over form factors are known to converge quite rapidly (see [9] and references therein). A very effective way to test this property is to use the exact sum rules [20,21] …”