Exact Results in Quantum Theory & Gravity

In the Standard Model of particle physics, the interaction of a particle with the Higgs boson is responsible for its mass generation. This principle is known as the Higgs mechanism. Fermions interact with the Higgs boson through a Yukawa coupling constant. The presences of a Higgs-like particle and the Yukawa coupling have now been confirmed at the CERN Large Hadron Collider (LHC). In this talk, I will discuss rigorous, non-perturbative proof of the fermion mass generation. I will start with a weakly coupled U(1) Higgs-Yukawa theory on a unit lattice in d=4 and show exponential decay of two-point fermion correlation function. This is the mass gap. Mass gap implies that all the particles in the theory i.e. the U(1) gauge boson, the Higgs boson and the fermions have a non-zero physical mass.
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