Speaker
Description
We provide the leading near conformal corrections on a cylinder to the scaling dimension of the lowest-lying fixed isospin charge $Q$ operators defined at the lower boundary of the Quantum Chromodynamics conformal window:
\begin{equation}
\tilde{\Delta}Q = \tilde{\Delta}_Q^\ast +\left(\frac{m{\sigma}}{4 \pi \nu}\right)^2 \, Q^{\frac{\Delta}{3}} B_1 + \left(\frac{m_\pi(\theta)}{4\pi \nu} \right)^4\ Q^{\frac{2}{3}(1-\gamma)} B_2 + \mathcal{O}\left ( m_\sigma^4 , m_\pi^8, m_\sigma^2 m_\pi^4\right) \ . \nonumber
\end{equation}
Here $\tilde{\Delta}_Q/r$ is the classical ground state energy of the theory on $\mathbb{R}\times S_r^3$ at fixed isospin charge while $\tilde{\Delta}_Q^\ast$ is the scaling dimension at the leading order in the large charge expansion. In the conformal limit $m_{\sigma}=m_\pi=0$ the state-operator correspondence implies $ \tilde{\Delta}_Q = \tilde{\Delta}_Q^\ast$.
The near-conformal corrections are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale $4\pi \nu$ with the $\theta$-angle dependence encoded directly in the pion mass. The characteristic $Q$-scaling is dictated by the quark mass operator anomalous dimension $\gamma$ and the one characterizing the dilaton potential $\Delta$. The coefficients $B_i$ with $i=1,2$ depend on the geometry of the cylinder and properties of the nearby conformal field theory.
