Charging the conformal window at nonzero <math display="inline"><mi>θ</mi></math> angle

We determine the impact of the <math display="inline"><mi>θ</mi></math> angle and axion physics on the near conformal dynamics of the large-charge baryon sector of <math display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> gauge theories with <math display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> fermions in the fundamental representation. We employ an effective approach featuring Goldstone and dilaton degrees of freedom augmented by the topological terms in the theory. We investigate how different dilaton potentials, including the ones for which a systematic counting scheme can be established, affect the results. Via state-operator correspondence we compute the corrections to the would-be conformal dimensions of the lowest large-charge operators as a function of the <math display="inline"><mi>θ</mi></math> term and dilaton potential.