Abstract
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.
Highlights
One of the simplest ways to conceive of a UV-complete QFT is to imagine the existence of a UV CFT fixed point, which is deformed by a relevant operator
As a final check of our proposal, we show explicitly that in integrable theories, the additional dressing factor (1.4) of the scattering matrix precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz (TBA) equations
We show, following [8], that the shifts (3.35) in the spectra can be recovered by applying the Thermodynamic Bethe Ansatz (TBA) equations [34] to the dressed S-matrix
Summary
One of the simplest ways to conceive of a UV-complete QFT is to imagine the existence of a UV CFT fixed point, which is deformed by a relevant operator. Soon afterwards, [10] provided a framework that unifies the exact solubility of the irrelevant T Tdeformation of general QFTs with the gravitational dressing procedure of the S-matrix This was achieved by reformulating the deformation as coupling the original QFT to a topological theory of gravity, in which the metric is allowed to fluctuate, but in a way that forces it to be everywhere flat. As a final check of our proposal, we show explicitly that in integrable theories, the additional dressing factor (1.4) of the scattering matrix precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz (TBA) equations. This confirms that the two predictions that follow from our general definition of J Ta-deformed QFTs are consistent with each other.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
