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We investigate the low energy continuum limit theory for electrons in agraphene sheet under strain. We use the quantum field theory in curved spacesto analyze the effect of the system deformations into an effective gauge field.We study both in-plane and out-of-plane deformations and obtain a closedexpression for the effective gauge field due to arbitrary nonuniform sheetdeformations. The obtained results reveal a remarkable relation between thelocal-pseudo magnetic field and the Riemann curvature, so far overlooked.

Gauge fields in graphene with nonuniform elastic deformations: A quantum field theory approach