Flows in the space of interacting chiral boson theories

We study interacting theories of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math> left-moving and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mover accent="true"><c:mi>N</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> right-moving Floreanini-Jackiw bosons in two dimensions. A parametrized family of such theories is shown to enjoy (nonmanifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root-<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>T</g:mi><g:mover accent="true"><g:mi>T</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math> deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>N</k:mi><k:mo>=</k:mo><k:mover accent="true"><k:mi>N</k:mi><k:mo stretchy="false">¯</k:mo></k:mover></k:math>, we consider the quantum effective action for the root-<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>T</o:mi><o:mover accent="true"><o:mi>T</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math>-deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>U</s:mi><s:mo stretchy="false">(</s:mo><s:mn>1</s:mn><s:mo stretchy="false">)</s:mo></s:math> Chern-Simons theories in three dimensions, which might be used to describe deformations of charged <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>AdS</w:mi><w:mn>3</w:mn></w:msub></w:math> black holes or quantum Hall systems. Published by the American Physical Society 2024