We develop an effective low-energy, long-wavelength theory of a bulksupersolid--a putative phase of matter with simultaneous crystallinity and Bosecondensation. Using conservation laws and general symmetry arguments we derivean effective action that correctly describes the coupling between the Bosecondensation and the elasticity of the solid. We use our effective action tocalculate the correlation and response functions for the supersolid, and weshow that the onset of supersolidity produces peaks in the response function,corresponding to propagating second sound modes in the solid. Throughout ourwork we make connections to existing work on effective theories of superfluidsand normal solids, and we underscore the importance of conservation laws andsymmetries in determining the number and character of the collective modes.
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