Abstract
We investigate the spontaneous breaking of subsystem symmetries directly in the context of continuum field theories by calculating the correlation function of charged operators. Our methods confirm the lack of spontaneous symmetry breaking in some of the existing continuum field theories with subsystem symmetries, as had previously been established based on a careful analysis of the spectrum. We present some novel continuum field theory constructions that do exhibit spontaneous symmetry breaking whenever allowed by general principles. These interesting patterns of symmetry breaking occur despite the fact that all the theories we study are non-interacting.
Highlights
Scalar, the standard (∂xφ)2 + (∂yφ)2 kinetic term gets replaced with (∂x∂yφ
We investigate the spontaneous breaking of subsystem symmetries directly in the context of continuum field theories by calculating the correlation function of charged operators
We present some novel continuum field theory constructions that do exhibit spontaneous symmetry breaking whenever allowed by general principles
Summary
Let us consider a field theory living in d spacetime dimensions with a subsystem symmetry acting on n dimensional submanifolds. The classical approach to diagnosing a spontaneously broken symmetry is to define a local order parameter that is charged under the symmetry, and calculate if this order parameter acquires an expectation value in the vacuum state. This computation is delicate as the expectation value of a charged operator vanishes for any finite size system which obeys the symmetry. A different approach to diagnosing spontaneous symmetry breaking is to compute the long range correlation functions of charged operators, and see if they vanish. We present an example of such a correlation function in the following subsection
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