Existence of a Mass Gap in SU(3) Yang-Mills Theory within the Simplicial Discrete Informational Spacetime Framework: A Strong Coupling Analysis

The existence of a mass gap in quantum Yang-Mills theory remains a fundamental open question in mathematical physics. This paper investigates this problem within the theoretical context provided by the Complete Theory of Simplicial Discrete Informational Spacetime (SDIS) (Karazoupis, 2025). This framework posits a fundamentally discrete, quantum-informational structure for spacetime based on a simplicial network. Adopting a Hamiltonian formulation analogous to lattice gauge theory but applied to the SDIS simplicial structure, the energy spectrum of the emergent pure SU(3) gauge theory is analyzed in the strong coupling limit (g → ∞), the regime associated with confinement. The unique, gauge-invariant vacuum state and its energy are identified through analysis of the Hamiltonian. Subsequently, the lowest-lying gauge-invariant excited state, corresponding to a minimal chromoelectric flux loop excitation (glueball), is identified and its energy calculated. By explicitly calculating the energy difference between this first excited state and the vacuum, it is demonstrated analytically that this energy gap is strictly positive (ΔE > 0) within this theoretical framework and approximation. This result shows that the SDIS framework inherently accommodates a mechanism for mass gap generation, suggesting a potential resolution to the mass gap problem if the SDIS framework is adopted as the underlying description of spacetime and gauge fields.