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arXiv:hep-th/0001097 · Nuclear Physics B

The intrinsic coupling in integrable quantum field theories

J. Balog, Max R. Niedermaier, F. Niedermayer, Adrian Patrascioiu, Erhard Seiler, P. Weisz

Published Sep 1, 2000• 19 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(00)00277-7

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A general definition of JTaJT_aJTa​ -- deformed QFTs
We propose a general path-integral definition of two-dimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a U(1) current. The deformed theory is obtained by coupling the original QFT to a flat dynamical gauge field and ``half'' a flat dynamical vielbein. The resulting partition function is shown to satisfy a geometric flow equation, which perfectly reproduces the flow equations for the deformed energy levels that were previously derived in the literature. The S-matrix of the deformed QFT differs from the original S-matrix only by an overall phase factor that depends on the charges and momenta of the external particles, thus supporting the conjecture that such QFTs are UV complete, although intrinsically non-local. For the special case of an integrable QFT, we check that this phase factor precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz equations.
Abstract In this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda field theories and the O ( N ) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb–Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O ( N ) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb–Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.