A String-EFT Hilbert-Polya Candidate: Deforming the Modular Laplacian via D7-Brane Matter Couplings

We propose a novel, physically motivated candidate for the Hilbert-Pólya conjecture, derived from the Effective Field Theory (EFT) of Type IIB string compactifications. We construct the kinetic operator of the axio-dilaton field on the modular surface SL(2,ℤ), represented by the Laplace-Beltrami operator Δ. We conjecture that higher-derivative string corrections from the D²ᵏR⁴ tower act as a self-adjoint deformation to this operator. Specifically, we define the potential V(z) via non-holomorphic Eisenstein series and propose the Hamiltonian H = -Δ + βV(z). The perturbation parameter is topologically locked to the D7-brane matter coupling β = -1/(2√2) ≈ -0.354. We hypothesize that this attractive potential explicitly deforms the Maass spectrum, shifting the eigenvalues of the modular Laplacian toward the non-trivial zeros of the Riemann zeta function. This framework bridges the gap between string phenomenology and the spectral theory of zeta functions, providing a testable Hamiltonian for the Riemann zeros.