Fractons and Exotic Symmetries from Branes

Abstract

The emerging study of fractons, a new type of quasi-particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of foliated field theories which, roughly, are built by coupling together fields supported on the leaves of foliations of spacetime. Another approach, which we refer to as exotic field theory, focuses on constructing Lagrangians consistent with special symmetries (like subsystem symmetries) that are adjacent to fracton physics. A third framework is that of infinite-component Chern-Simons theories, which attempts to generalize the role of conventional Chern-Simons theory in describing (2+1)D Abelian topological order to fractonic order in (3+1)D. The study of these theories is ongoing, and many of their properties remain to be understood. Historically, it has been fruitful to study QFTs by embedding them into string theory. One way this can be done is via D-branes, extended objects whose dynamics can, at low energies, be described in terms of conventional quantum field theory. QFTs that can be realized in this way can then be analyzed using the rich mathematical and physical structure of string theory. In this paper, we show that foliated field theories, exotic field theories, and infinite-component Chern-Simons theories can all be realized on the world-volumes of branes. We hope that these constructions will ultimately yield valuable insights into the physics of these interesting field theories.

Space-Dependent Symmetries and Fractons

“…This construction allows us to give a geometric interpretation to the Nambu-Goldstone boson associated to the spontaneous symmetry breaking in systems with monopole and dipole charge conservation, and naturally predicts the linear shift transformations of the gapless low energy mode ϕ. Notice also that in [32], Geng, Kachru, Karch, Nally and Rayhaun studied fracton theories from brane constructions. Nonetheless, there is no obvious relation between their models and the Heisenberg space picture discussed here.…”

“…It should be noted that emergent subsystem symmetries and fractonic dispersion relations are not limited to theories with a global vector symmetry (or other polynomial shift symmetries), they may also appear in other situations, such as the model with spontaneously broken translation invariance studied by Argurio, Hoyos, Musso and Naegels [74]. Exact subsystem symmetries can be realized in a variety of continuum theories [75][76][77][78][79][80][81][82][83][84][85] (see [32] for a nice summary).…”

Fractons, geometrically

“…Thus, the massless spinor is also fractonic, like (39). In addition, the dualisation of the strain-Maxwell model ( 29) and the connection to D-branes, following [26][27][28][29][30][31][32][33][34] and [23], deserve further study.…”

Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions

“…(See also Ref. [102] for a spiritually similar supersymmetric U(1) construction which arises on the world-volumes of branes in string theory.) Our ultimate aim, as we stated earlier, is to study the fate of the subsystem symmetry breaking phase transition of decoupled Ising wires after they are coupled to the bulk topological gauge theory.…”