Speaker
Description
We develop a conformal formulation of small-$x$ QCD at the Wilson--Fisher point $d=4-2\epsilon_\ast$. In $d=4$ the LO BK kernel is M\"obius invariant, and at the critical coupling the BK/BFKL evolution \emph{remains} conformal through NLO (with the appropriate composite/conformal dipole), yielding power-law eigenfunctions, an explicitly organized $b_0$ dependence, and a shifted Pomeron intercept. Matching a four-point correlator in the Regge/light-cone double limit recovers the standard BFKL--DGLAP consistency relation that ties the intercept to twist-2 anomalous dimensions of gluon light-ray operators—showing, in particular, that in $\overline{\mathrm{MS}}$ the anomalous dimensions at $d=4-2\epsilon_\ast$ coincide with those at $d=4$, even though the intercept differs. The framework unifies resummation (BFKL/NLL), evolution (BK/DGLAP), and factorization (high-energy OPE) with an explicit treatment of the rapidity regulator, and it suggests a route to NNLO information via $O(\epsilon)$ pieces of NLO BK $\to O(\alpha_s^2 b_0)$ terms.
