Charge as Topological Entanglement: Emergent QED from Anyon Condensation

The Standard Model (SM) treats electric charge as a fundamental input parameter and postulates U(1) gauge symmetry, leaving the quantization of charge and the origin of the electromagnetic field without a first-principles explanation. In this paper we propose that charge is not a fundamental attribute, but a topological quantum number generated by the braiding statistics between boundary anyons and bulk excitations in a string-net condensate. Based on the modular tensor category (MTC) C=SU(3)3×SU(2)2 and the condensation algebra A=1⊕(3,0)⊕(0,3), we show that in the low-energy effective limit the boundary physics is dominated by the Ising category corresponding to the SU(2)2 factor. We identify real photons as free transverse vibration modes of the bulk string network, and electrons and positrons as conjugate boundary Ising flows σ. We show that electron-positron pair creation is a topological splitting process mediated by the condensation algebra, and that charge quantization (including the 1/3 fractional charge of quarks) originates from the discrete triality structure of the SU(3)3 category. We rigorously compute the bulk-boundary topological entanglement strength |Cγ,σ |2=2√2. This strength is fixed exactly by the Ising boundary s-matrix after Z3 condensation, and is the exact value of the topological entanglement between the bulk gauge mode and the boundary σ flow. Finally, we show that the induced gauge field (virtual photon) in the low-energy limit exactly reproduces the QED photon propagator; by relating the charge entanglement to the emergent SU(2)2 boundary algebra, we locate charge and QED within the electroweak algebra.