[1] R.M. Nandkishore and M. Hermele, Fractons, Ann. Rev. Cond. Matter Phys. 10 (2019) 295
[arXiv:1803.11196] [INSPIRE].
[2] M. Pretko, X. Chen and Y. You, Fracton Phases of Matter, Int. J. Mod. Phys. A 35 (2020)
2030003 [arXiv:2001.01722] [INSPIRE].
– 26 –
JHEP03(2023)188
chiral φ-theory. We finally discussed vacuum structures of the theories including fermions
and found that the vacua are infinitely degenerate.
There are various interesting directions for future. We have seen that the models
discussed in this paper have common features to ordinary (1+1)-dimensional field theories.
Therefore it would be interesting to see whether or not there are other common phenomena
such as bosonization, anomalies and index theorem. We also discussed the analogues of
the chiral boson and chiral fermion while a precise meaning of “chirality” in this context is
still unclear. It would be interesting if one finds an appropriate definition of the “chirality”.
It should be also important to study the “doubling problem” in lattice regularization
of fermionic theories with subsystem symmetries in more detail. In particular this paper
proposed only one prescription by an analogue of Wilson fermion while there should be
other ways to avoid the problem such as analogues of Staggered, overlap and domain wall
fermions. It would be also illuminating to see whether there is an analogue of the NielsenNinomiya theorem [31, 32] for field theories with subsystem symmetries.
Many of ordinary field theories can be realized as worldvolume theories of D-branes in
string theory. Recently some field theories with subsystem symmetries were constructed
from brane constructions [23]. It would be interesting to ask whether field theories discussed
in this paper or their extensions have connections to string theory as well as quiver gauge
theories [22, 33] and gravity [34–37].
In some spin models with fracton excitations, phases are characterized by the foliation
structure of spatial manifold [38, 39]. There have been many works on the field theories
which describe these phases, which are called “foliated fracton phases” [40–42]. In recent
work [43], it was reported that one of such field theories have correspondence with the
gauge field coming from subsystem symmetries. It would be important to study about
excitations in foliated theories and find a correspondence with the theories studied in this
paper. Last but not least, there should be various interesting directions in future related
to other recent progress [12–15, 44–54].
[3] S. Vijay, J. Haah and L. Fu, A New Kind of Topological Quantum Order: A Dimensional
Hierarchy of Quasiparticles Built from Stationary Excitations, Phys. Rev. B 92 (2015)
235136 [arXiv:1505.02576] [INSPIRE].
[4] A. Paramekanti, L. Balents and M.P.A. Fisher, Ring exchange, the exciton Bose liquid, and
bosonization in two dimensions, Phys. Rev. B 66 (2002) 054526.
[5] C. Chamon, Quantum Glassiness, Phys. Rev. Lett. 94 (2005) 040402 [cond-mat/0404182]
[INSPIRE].
[6] J. Haah, Local stabilizer codes in three dimensions without string logical operators, Phys.
Rev. A 83 (2011) 042330 [arXiv:1101.1962] [INSPIRE].
[8] N. Seiberg and S.-H. Shao, Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional
Quantum Field Theory, SciPost Phys. 10 (2021) 027 [arXiv:2003.10466] [INSPIRE].
[9] N. Seiberg and S.-H. Shao, Exotic U (1) Symmetries, Duality, and Fractons in
3+1-Dimensional Quantum Field Theory, SciPost Phys. 9 (2020) 046 [arXiv:2004.00015]
[INSPIRE].
[10] N. Seiberg and S.-H. Shao, Exotic ZN symmetries, duality, and fractons in 3+1-dimensional
quantum field theory, SciPost Phys. 10 (2021) 003 [arXiv:2004.06115] [INSPIRE].
[11] P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, More Exotic Field Theories in 3+1
Dimensions, SciPost Phys. 9 (2020) 073 [arXiv:2007.04904] [INSPIRE].
[12] P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, fcc lattice, checkerboards, fractons, and
quantum field theory, Phys. Rev. B 103 (2021) 205116 [arXiv:2010.16414] [INSPIRE].
[13] T. Rudelius, N. Seiberg and S.-H. Shao, Fractons with Twisted Boundary Conditions and
Their Symmetries, Phys. Rev. B 103 (2021) 195113 [arXiv:2012.11592] [INSPIRE].
[14] P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, A modified Villain formulation of fractons
and other exotic theories, J. Math. Phys. 62 (2021) 102301 [arXiv:2103.01257] [INSPIRE].
[15] P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, Low-energy limit of some exotic lattice
theories and UV/IR mixing, Phys. Rev. B 104 (2021) 235116 [arXiv:2108.00020] [INSPIRE].
[16] S. Yamaguchi, Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions
and fermionic fracton phases, PTEP 2021 (2021) 063B04 [arXiv:2102.04768] [INSPIRE].
[17] F.J. Burnell et al., Anomaly inflow for subsystem symmetries, Phys. Rev. B 106 (2022)
085113 [arXiv:2110.09529] [INSPIRE].
[18] S. Yamaguchi, Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge
theory and anomaly inflow for subsystem symmetry, PTEP 2022 (2022) 033B08
[arXiv:2110.12861] [INSPIRE].
[19] Y. You and F. von Oppen, Majorana Quantum Lego, a Route Towards Fracton Matter, Phys.
Rev. Research. 1 (2019) 013011 [arXiv:1812.06091] [INSPIRE].
[20] N. Tantivasadakarn, Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any
Dimension: Emergent Fermions in Fracton Topological Order, Phys. Rev. Res. 2 (2020)
023353 [arXiv:2002.11345] [INSPIRE].
[21] W. Shirley, Fractonic order and emergent fermionic gauge theory, arXiv:2002.12026
[INSPIRE].
– 27 –
JHEP03(2023)188
[7] N. Seiberg, Field Theories With a Vector Global Symmetry, SciPost Phys. 8 (2020) 050
[arXiv:1909.10544] [INSPIRE].
[22] S.S. Razamat, Quivers and Fractons, Phys. Rev. Lett. 127 (2021) 141603
[arXiv:2107.06465] [INSPIRE].
[23] H. Geng et al., Fractons and Exotic Symmetries from Branes, Fortsch. Phys. 69 (2021)
2100133 [arXiv:2108.08322] [INSPIRE].
[24] J. Distler, A. Karch and A. Raz, Spontaneously broken subsystem symmetries, JHEP 03
(2022) 016 [arXiv:2110.12611] [INSPIRE].
[25] H. Katsura and Y. Nakayama, Spontaneously broken supersymmetric fracton phases with
fermionic subsystem symmetries, JHEP 08 (2022) 072 [arXiv:2204.01924] [INSPIRE].
[27] S. Bellucci, R. Brooks and J. Sonnenschein, Supersymmetric chiral bosons, Nucl. Phys. B
304 (1988) 173 [INSPIRE].
[28] J. Sonnenschein, Chiral bosons, Nucl. Phys. B 309 (1988) 752 [INSPIRE].
[29] S. Yamaguchi, SL(2, Z) action on quantum field theories with U(1) subsystem symmetry,
arXiv:2208.13193 [OU-HET 1153] [INSPIRE].
[30] J. Distler, M. Jafry, A. Karch and A. Raz, Interacting fractons in 2+1-dimensional quantum
field theory, JHEP 03 (2022) 070 [arXiv:2112.05726] [INSPIRE].
[31] H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. 1. Proof by Homotopy
Theory, Nucl. Phys. B 185 (1981) 20 [Erratum ibid. 195 (1982) 541] [INSPIRE].
[32] H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. 2. Intuitive Topological
Proof, Nucl. Phys. B 193 (1981) 173 [INSPIRE].
[33] S. Franco and D. Rodriguez-Gomez, Quivers, Lattice Gauge Theories, and Fractons, Phys.
Rev. Lett. 128 (2022) 241603 [arXiv:2203.01335] [INSPIRE].
[34] M. Pretko, Emergent gravity of fractons: Mach’s principle revisited, Phys. Rev. D 96 (2017)
024051 [arXiv:1702.07613] [INSPIRE].
[35] V. Benedetti, H. Casini and J.M. Magan, Generalized symmetries of the graviton, JHEP 05
(2022) 045 [arXiv:2111.12089] [INSPIRE].
[36] V. Benedetti, H. Casini and J.M. Magan, Generalized symmetries and Noether’s theorem in
QFT, JHEP 08 (2022) 304 [arXiv:2205.03412] [INSPIRE].
[37] K. Hinterbichler, D.M. Hofman, A. Joyce and G. Mathys, Gravity as a gapless phase and
biform symmetries, JHEP 02 (2023) 151 [arXiv:2205.12272] [INSPIRE].
[38] W. Shirley, K. Slagle, Z. Wang and X. Chen, Fracton Models on General Three-Dimensional
Manifolds, Phys. Rev. X 8 (2018) 031051 [arXiv:1712.05892] [INSPIRE].
[39] J.M. Torres-Rincon, Chiral symmetry restoration with three chiral partners, SciPost Phys.
Proc. 6 (2022) 015 [arXiv:2112.09463] [INSPIRE].
[40] K. Slagle, D. Aasen and D. Williamson, Foliated Field Theory and String-Membrane-Net
Condensation Picture of Fracton Order, SciPost Phys. 6 (2019) 043 [arXiv:1812.01613]
[INSPIRE].
[41] K. Slagle, Foliated Quantum Field Theory of Fracton Order, Phys. Rev. Lett. 126 (2021)
101603 [arXiv:2008.03852] [INSPIRE].
– 28 –
JHEP03(2023)188
[26] W. Cao, M. Yamazaki and Y. Zheng, Boson-fermion duality with subsystem symmetry, Phys.
Rev. B 106 (2022) 075150 [arXiv:2206.02727] [INSPIRE].
[42] P.-S. Hsin and K. Slagle, Comments on foliated gauge theories and dualities in 3+1d, SciPost
Phys. 11 (2021) 032 [arXiv:2105.09363] [INSPIRE].
[43] K. Ohmori and S. Shimamura, Foliated-Exotic Duality in Fractonic BF Theories,
arXiv:2210.11001 [INSPIRE].
[44] R. Casalbuoni, J. Gomis and D. Hidalgo, Worldline description of fractons, Phys. Rev. D
104 (2021) 125013 [arXiv:2107.09010] [INSPIRE].
[45] S. Angus, M. Kim and J.-H. Park, Fractons, non-Riemannian geometry, and double field
theory, Phys. Rev. Res. 4 (2022) 033186 [arXiv:2111.07947] [INSPIRE].
[47] P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, Global dipole symmetry, compact Lifshitz
theory, tensor gauge theory, and fractons, Phys. Rev. B 106 (2022) 045112
[arXiv:2201.10589] [INSPIRE].
[48] K. Jensen and A. Raz, Large N fractons, arXiv:2205.01132 [INSPIRE].
[49] A. Pérez and S. Prohazka, Asymptotic symmetries and soft charges of fractons, Phys. Rev. D
106 (2022) 044017 [arXiv:2203.02817] [INSPIRE].
[50] Y. Hirono, M. You, S. Angus and G.Y. Cho, A symmetry principle for gauge theories with
fractons, arXiv:2207.00854 [RIKEN-iTHEMS-Report-22] [INSPIRE].
[51] P. Gorantla, H.T. Lam and S.-H. Shao, Fractons on graphs and complexity, Phys. Rev. B
106 (2022) 195139 [arXiv:2207.08585] [INSPIRE].
[52] H. Ebisu and B. Han, Anisotropic higher rank ZN topological phases on graphs,
arXiv:2209.07987 [INSPIRE].
[53] P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, 2+1d Compact Lifshitz Theory, Tensor
Gauge Theory, and Fractons, arXiv:2209.10030 [MIT-CTP/5462] [INSPIRE].
[54] P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, Gapped lineon and fracton models on
graphs, Phys. Rev. B 107 (2023) 125121 [arXiv:2210.03727] [INSPIRE].
– 29 –
JHEP03(2023)188
[46] A. Jain and K. Jensen, Fractons in curved space, SciPost Phys. 12 (2022) 142
[arXiv:2111.03973] [INSPIRE].
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