Abstract
We consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally nonvanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a nondynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behavior of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.
Highlights
We consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect
Depending on how the deformation is done, the resulting geometry acquires a locally nonvanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a nondynamical gauge field
We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behavior of the order parameter in the vicinity of the defect
Summary
A interesting corner of this intersection is that of QFTs featuring spontaneous symmetry breaking, where effects of curved space are expected to alter the way vacuum destabilization and phase transitions take place. Green’s functions on these backgrounds enjoy a periodicity with period set by the horizon size, analogous to thermal Green’s functions for which the period is set by the inverse temperature This leads to the expectation that for a sufficiently small horizon a transition from a broken to a symmetric phase may occur. These arguments have been made quantitatively in a number of cases, with some initial discussions focusing on scalar fields and spatially homogeneous backgrounds
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