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

Gorantla, Pranay; Lam, Ho Tat; Seiberg, Nathan; Shao, Shu-Heng

doi:10.48550/arxiv.2201.10589

Cited by 18 publications

(64 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similarly, the GSD of the color code model [29,30] is also sensitive to the system size of a hexagonal lattice based on whether or not the lattice is globally tricolorable. Furthermore, recently Seiberg et al have found the GSD of several different models to depend on the the greatest common divisor between the system size and N [65,66]. In particular, as a consequence of possessing a Z N global dipole symmetry, the 1 + 1d "Z N tensor gauge theory" they study is closely related to the gauge charge sector of the rank-2 toric code.…”

Section: Ground State Degeneracymentioning

confidence: 99%

See 1 more Smart Citation

Position-Dependent Excitations and UV/IR Mixing in the $\mathbb{Z}_{N}$ Rank-2 Toric Code and its Low-Energy Effective Field Theory

Pace,

Wen

2022

Preprint

View full text Add to dashboard Cite

We investigate how symmetry and topological order are coupled in the 2 + 1d ZN rank-2 toric code for general N , which is an exactly solvable point in the Higgs phase of a symmetric rank-2 U (1) gauge theory. The symmetry enriched topological order present has a non-trivial realization of square-lattice translation (and rotation/reflection) symmetry, where anyons on different lattice sites have different types and belong to different superselection sectors. We call such particles "position-dependent excitations." As a result, in the rank-2 toric code anyons can hop by one lattice site in some directions while only by N lattice sites in others, reminiscent of fracton topological order in 3 + 1d. We find that while there are N 2 flavors of e charges and 2N flavors of m fluxes, there are not N N 2 +2N anyon types. Instead, there are N 6 anyon types, and we can use Chern-Simons theory with six U (1) gauge fields to describe all of them. While the lattice translations permute anyon types, we find that such permutations cannot be expressed as transformations on the six U (1) gauge fields. Thus the realization of translation symmetry in the U 6 (1) Chern-Simons theory is not known. Despite this, we find a way to calculate the translation-dependent properties of the theory. In particular, we find that the ground state degeneracy on an Lx × Ly torus is N 3 gcd(Lx, N ) gcd(Ly, N ) gcd(Lx, Ly, N ), where gcd stands for "greatest common divisor." We argue that this is a manifestation of UV/IR mixing which arises from the interplay between lattice symmetries and topological order.

show abstract

Section: Ground State Degeneracymentioning

confidence: 99%

“…Therefore, any low-energy effective field theory must make explicit mention to the lattice spacing and number of lattice sites (which we'll indeed find to be true in Section III C). This can be interpreted as a manifestation of UV/IR mixing [65,66], where the low-energy (IR) physics cannot be decoupled from the FIG. 5.…”

Section: Ground State Degeneracymentioning

confidence: 99%

Position-Dependent Excitations and UV/IR Mixing in the $\mathbb{Z}_{N}$ Rank-2 Toric Code and its Low-Energy Effective Field Theory

Pace,

Wen

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The fracton particles are charged under the higher-rank gauge symmetry, and their motion is constrained by the multipole moment conservation from the gauge symmetry. More precisely, the restricted mobility can be explained as a consequence of a global symmetry that acts on the Wilson defects, which represent the worldlines of infinitely heavy fracton particles, in higher-rank gauge theory [121]. See [48, for other developments in higher-rank gauge theory.…”

Section: Exotic Field Theories For Fractonsmentioning

confidence: 99%

Snowmass White Paper: Effective Field Theories for Condensed Matter Systems

Brauner¹,

Hartnoll²,

Kovtun³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high energy physics and many-body theory. We discuss developments in the effective field theory of spontaneous symmetry breaking, of hydrodynamics and non-equilibrium dynamics more generally, fracton phases of matter, and dualities between 2+1 dimensional field theories. We furthermore discuss the application of effective field theory to non-Fermi liquids, the dynamics of entanglement entropy and to condensed matter aspects of cosmology.

show abstract

“…For further insightful remarks and an interesting complementary analysis of dipole charges, see[21].…”

mentioning

confidence: 99%

Asymptotic symmetries and soft charges of fractons

Pérez¹,

Prohazka²

2022

Preprint

View full text Add to dashboard Cite

The asymptotic structure of gauge theories describing fracton interactions is analyzed. Two sets of asymptotic conditions are proposed. Both encompass all known solutions, lead to finite charges and resolve the problem of the divergent energy coming from the monopole contribution. While the first set leads to the expected fracton symmetry algebra, including a dipole charge, the second set provides a soft infinite-dimensional extension of it. These soft charges provide evidence of a rich infrared structure for fracton-like theories and provide one corner of a possible fracton infrared triangle.

show abstract

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

Cited by 18 publications

References 67 publications

Position-Dependent Excitations and UV/IR Mixing in the $\mathbb{Z}_{N}$ Rank-2 Toric Code and its Low-Energy Effective Field Theory

Position-Dependent Excitations and UV/IR Mixing in the $\mathbb{Z}_{N}$ Rank-2 Toric Code and its Low-Energy Effective Field Theory

Snowmass White Paper: Effective Field Theories for Condensed Matter Systems

Asymptotic symmetries and soft charges of fractons

Contact Info

Product

Resources

About