publication . Preprint . 2019

Higher-Rank Non-Abelian Tensor Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauge

Wang, Juven; Xu, Kai; Yau, Shing-Tung;
Open Access English
  • Published: 29 Oct 2019
With a view toward a theory of fracton and embeddon in condensed matter, we introduce a higher-moment polynomial degree-(m-1) global symmetry, acting on complex scalar/vector/tensor fields. We relate this higher-moment global symmetry of $n$-dimensional space, to a lower degree (either ordinary or higher-moment, e.g., degree-(m-1-$\ell$)) subdimensional or subsystem global symmetry on layers of $(n-\ell)$-submanifolds. These submanifolds are algebraic affine varieties (i.e., solutions of polynomials). The structure of layers of submanifolds as subvarieties can be studied via mathematical tools of embedding, foliation and algebraic geometry. We also generalize No...
free text keywords: High Energy Physics - Theory, Condensed Matter - Strongly Correlated Electrons, Mathematical Physics
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40 references, page 1 of 3

[1] R. M. Nandkishore and M. Hermele, Fractons, Ann. Rev. Condensed Matter Phys. 10 295-313 (2019), [arXiv:1803.11196].

[2] J. Wang and K. Xu, Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon, arXiv:1909.13879.

[3] H. Weyl, Electron and Gravitation. 1. (In German), Z. Phys. 56 330-352 (1929).

[4] R. Dijkgraaf and E. Witten, Topological Gauge Theories and Group Cohomology, Commun.Math.Phys. 129 393 (1990).

[5] M. Kalb and P. Ramond, Classical direct interstring action, Phys. Rev. D9 2273-2284 (1974). [OpenAIRE]

[6] J. Wang, X.-G. Wen and S.-T. Yau, Quantum Statistics and Spacetime Surgery, arXiv:1602.05951.

[7] P. Putrov, J. Wang and S.-T. Yau, Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions, Annals Phys. 384 254-287 (2017), [arXiv:1612.09298].

[8] J. Wang, K. Ohmori, P. Putrov, Y. Zheng, Z. Wan, M. Guo et al., Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions, PTEP 2018 053A01 (2018), [arXiv:1801.05416].

[9] J. Wang, X.-G. Wen and S.-T. Yau, Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas, Annals Phys. 409 167904 (2019), [arXiv:1901.11537].

[10] A. Kapustin and R. Thorngren, Anomalies of discrete symmetries in various dimensions and group cohomology, arXiv:1404.3230.

[11] J. C. Wang, Z.-C. Gu and X.-G. Wen, Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond, Phys. Rev. Lett. 114 031601 (2015), [arXiv:1405.7689].

[12] A. Rasmussen, Y.-Z. You and C. Xu, Stable Gapless Bose Liquid Phases without any Symmetry, arXiv e-prints arXiv:1601.08235 (2016 Jan), [arXiv:1601.08235].

[13] M. Pretko, Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids, Phys. Rev. B95 115139 (2017), [arXiv:1604.05329]. [OpenAIRE]

[14] M. Pretko, Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story, Phys. Rev. B96 035119 (2017), [arXiv:1606.08857].

[15] M. Pretko, Higher-Spin Witten Effect and Two-Dimensional Fracton Phases, Phys. Rev. B96 125151 (2017), [arXiv:1707.03838].

40 references, page 1 of 3
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