Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Understand

We study field theories with global dipole symmetries and gauge dipole symmetries.

• The famous Lifshitz theory is an example of a theory with a global dipole symmetry.
• We study in detail its 1+1d version with a compact field.
• When this global symmetry is promoted to a $U(1)$ dipole gauge symmetry, the corresponding gauge field is a tensor gauge field.