The fermion bag is a powerful idea that helps to solve fermion lattice field theories using Monte Carlo methods. Some sign problems that had remained unsolved earlier can be solved within this framework. In this work we argue that the fermion bag also gives insight into a new mechanism of fermion mass generation, especially at strong couplings where fermion masses are related to the fermion bag size. On the other hand, chiral condensates arise due to zero modes in the Dirac operator within a fermion bag. Although in traditional four-fermion models the two quantities seem to be related, we show that they can be decoupled. While fermion bags become small at strong couplings, the ability of zero modes of the Dirac operator within fermion bags to produce a chiral condensate, can be suppressed by the presence of additional zero modes from other fermions. Thus, fermions can become massive even without a chiral condensate. This new mechanism of mass generation was discovered long ago in lattice field theory, but has remained unappreciated. Recent work suggests that it may be of interest even in continuum quantum field theory.
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