Abstract
In two recent papers [1, 2] we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised \( \textrm{T}\overline{\textrm{T}} \)-deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to \( \textrm{T}\overline{\textrm{T}} \)-perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for \( \textrm{T}\overline{\textrm{T}} \)-perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of the recent publication [3] where the same problem has been addressed.
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Acknowledgments
The authors thank Benjamin Doyon and Michele Mazzoni for useful discussions. Olalla A. Castro-Alvaredo thanks EPSRC for financial support under Small Grant EP/W007045/1. The work of Stefano Negro is supported by the NSF grant PHY-2210349 and by the Simons Collaboration on Confinement and QCD Strings. Fabio Sailis is grateful for his PhD Studentship which is funded by City, University of London.
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Castro-Alvaredo, O.A., Negro, S. & Sailis, F. Entanglement entropy from form factors in \( \textrm{T}\overline{\textrm{T}} \)-deformed integrable quantum field theories. J. High Energ. Phys. 2023, 129 (2023). https://doi.org/10.1007/JHEP11(2023)129
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DOI: https://doi.org/10.1007/JHEP11(2023)129