Abstract
We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the lambda Toverline{T} deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each field, with a Dirac-like string being attached at each infinitesimal step. The deformation then acts as a derivation on the whole operator algebra, satisfying the Leibniz rule. We derive an explicit equation which allows for the analysis of UV divergences, which may be absorbed into a non-local field renormalization to give correlation functions which are UV finite to all orders, satisfying a (deformed) operator product expansion and a Callan-Symanzik equation. We solve this in the case of a deformed CFT, showing that the Fourier-transformed renormalized two-point functions behave as k2∆+2λk2, where ∆ is their IR conformal dimension. We discuss in detail deformed Noether currents, including the energy-momentum tensor, and show that, although they also become non-local, when suitably improved they remain finite, conserved and satisfy the expected Ward identities. Finally, we discuss how the equivalence of the Toverline{T} deformation to a state-dependent coordinate transformation emerges in this picture.
Highlights
A torus [5, 6] and the related finite-size energy spectrum [1], the thermodynamics, the spectrum of asymptotic states in a massive theory, and their S-matrix which acquires only CDD phase factors [7,8,9]
We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the λT T deformation, suitably regularized
We derive an explicit equation which allows for the analysis of UV divergences, which may be absorbed into a non-local field renormalization to give correlation functions which are UV finite to all orders, satisfying a operator product expansion and a Callan-Symanzik equation
Summary
In order to see the structure of the integral J1 ∧ J2 d2x, it is useful first to examine the first order in perturbation theory in λ about a CFT. Note that the correlation function between m and n vanishes if both vorticities are zero It is worth noting directly from (2.12) that the coefficient of the log |ε| divergence is (λ/4π) abqnaqnb log |ε|. The origin of this logarithmic divergence may be traced to the singular terms in the OPE (2.7) with the source fields abJzaJzb ∼ abqnaqnb /zz + · · ·. Note that these terms are prescribed by the Ward identity and exist independently of perturbation theory
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.
