In BCS theory, the pairing instability is exponentially suppressed. Electrons attract each other through phonon exchange, but the coupling is weak, and the transition temperature goes as T_c ~ exp(-1/g). The exponential makes everything hard: small coupling produces vanishingly small critical temperatures, and explaining high-T_c superconductivity requires either implausibly strong coupling or an entirely different mechanism.
The suppression comes from the time structure of dissipation. Overdamped collective modes near a quantum critical point produce Ohmic damping — the response is proportional to frequency, which means the system forgets perturbations at a rate proportional to how fast they oscillate. Cooper pairs form when two electrons scatter repeatedly off the same fluctuation, but Ohmic dissipation washes out the fluctuation before the second electron arrives. The pairing channel is technically marginal: the RG flow goes as dg/dl ~ g^2, a slow logarithmic accumulation that produces the exponential in T_c.
Chae (arXiv 2602.22626, February 2026) proposes that near quantum critical points, the dissipation isn't Ohmic. When the spectrum of relaxation rates has a flat density of states at zero frequency — an extensive accumulation of nearly marginal collective modes — the memory kernel of the system goes as K(t) ~ 1/t instead of decaying exponentially. The system remembers. Not permanently, but algebraically: perturbations at time zero still influence the dynamics at time t with amplitude 1/t rather than exp(-t/tau).
This changes the pairing instability from marginal to relevant. The modified RG flow goes as dg/dl ~ alpha g instead of g^2. The solution is exponential growth rather than logarithmic accumulation, and the critical temperature becomes algebraic: T_c ~ rho_0 E_pair, where rho_0 is the spectral weight of the slow modes. No exponential suppression. The transition temperature is set by the density of slow modes, not by an inverse coupling constant buried inside an exponential.
The mechanism is physically transparent. A flat density of relaxation rates means there's always a mode with the right timescale to mediate pairing at any frequency. In the Ohmic case, fast modes dissipate and slow modes are frozen — there's a gap in the temporal matching. The 1/t kernel fills this gap. Each Cooper scattering event encounters fluctuations that haven't decayed yet, because the algebraic memory keeps them alive long enough for the second electron to arrive.
The framework produces superconducting domes naturally: the flat density of states exists at the quantum critical point but develops a gap away from it, cutting off the slow-mode reservoir and suppressing T_c. It predicts Uemura scaling (T_c proportional to superfluid density) from the same parameter rho_0 that controls both. And the same 1/t kernel generates the anomalous normal-state dynamics — strange-metal resistivity, 1/f noise, long-time correlations — observed above T_c in cuprates and heavy-fermion systems.
The gap in the argument is where the flat density of states comes from. The paper assumes it arises generically near quantum critical points, but doesn't derive it from any microscopic Hamiltonian. No Hubbard model calculation, no numerical simulation, no comparison to specific materials. The claim is that whenever you approach a quantum critical point in a correlated system, the spectrum of relaxation rates necessarily flattens at zero frequency. This may be true — the physical picture of an extensive continuum of nearly marginal modes near criticality is plausible — but it's asserted, not demonstrated.
The RG argument itself is clean. The conversion from g^2 to alpha * g through the modified infrared shell integral is a genuine and nontrivial result. If the flat density of states exists, the consequences follow mathematically. The question is whether the premise holds in real materials, and answering that requires the kind of microscopic calculation the paper doesn't provide.
The dissipation structure of a system determines whether its instabilities are exponentially suppressed or algebraically accessible. BCS assumed Ohmic dissipation and got exponential suppression. If the dissipation remembers — if the kernel goes as 1/t instead of decaying away — the same instability becomes algebraic. The pairing mechanism doesn't change. What changes is whether the system forgets the perturbation before the pair can form.