Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases
We study the quantized topological terms in a weak-coupling gauge theory with gauge group G[subscript g] and a global symmetry G[subscript s] in d space-time dimensions. We show that the quantized topological terms are classified by a pair (G,ν[subscript d]), where G is an extension of G[subscript s...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/88752 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1811081750139371520 |
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| author | Hung, Ling-Yan Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Hung, Ling-Yan Wen, Xiao-Gang |
| author_sort | Hung, Ling-Yan |
| collection | MIT |
| description | We study the quantized topological terms in a weak-coupling gauge theory with gauge group G[subscript g] and a global symmetry G[subscript s] in d space-time dimensions. We show that the quantized topological terms are classified by a pair (G,ν[subscript d]), where G is an extension of G[subscript s] by G[subscript g] and ν[subscript d] an element in group cohomology H[superscript d](G,R/Z). When d = 3 and/or when G[subscript g] is finite, the weak-coupling gauge theories with quantized topological terms describe gapped symmetry enriched topological (SET) phases (i.e., gapped long-range-entangled phases with symmetry). Thus, those SET phases are classified by H[superscript d](G,R/Z), where G/G[subscript g] = G[subscript s]. We also apply our theory to a simple case G[subscript s] = G[subscript g] = Z[subscript 2], which leads to 12 different SET phases in 2 + 1 dimensions [(2 + 1)D], where quasiparticles have different patterns of fractional G[subscript s] = Z[subscript 2] quantum numbers and fractional statistics. If the weak-coupling gauge theories are gapless, then the different quantized topological terms may describe different gapless phases of the gauge theories with a symmetry G[subscript s], which may lead to different fractionalizations of G[subscript s] quantum numbers and different fractional statistics [if in (2 + 1)D]. |
| first_indexed | 2024-09-23T11:51:34Z |
| format | Article |
| id | mit-1721.1/88752 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:51:34Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/887522022-09-27T22:26:23Z Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases Hung, Ling-Yan Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang We study the quantized topological terms in a weak-coupling gauge theory with gauge group G[subscript g] and a global symmetry G[subscript s] in d space-time dimensions. We show that the quantized topological terms are classified by a pair (G,ν[subscript d]), where G is an extension of G[subscript s] by G[subscript g] and ν[subscript d] an element in group cohomology H[superscript d](G,R/Z). When d = 3 and/or when G[subscript g] is finite, the weak-coupling gauge theories with quantized topological terms describe gapped symmetry enriched topological (SET) phases (i.e., gapped long-range-entangled phases with symmetry). Thus, those SET phases are classified by H[superscript d](G,R/Z), where G/G[subscript g] = G[subscript s]. We also apply our theory to a simple case G[subscript s] = G[subscript g] = Z[subscript 2], which leads to 12 different SET phases in 2 + 1 dimensions [(2 + 1)D], where quasiparticles have different patterns of fractional G[subscript s] = Z[subscript 2] quantum numbers and fractional statistics. If the weak-coupling gauge theories are gapless, then the different quantized topological terms may describe different gapless phases of the gauge theories with a symmetry G[subscript s], which may lead to different fractionalizations of G[subscript s] quantum numbers and different fractional statistics [if in (2 + 1)D]. National Science Foundation (U.S.) (Grant DMR-1005541) 2014-08-18T15:13:21Z 2014-08-18T15:13:21Z 2013-04 2012-12 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/88752 Hung, Ling-Yan, and Xiao-Gang Wen. “Quantized Topological Terms in Weak-Coupling Gauge Theories with a Global Symmetry and Their Connection to Symmetry-Enriched Topological Phases.” Phys. Rev. B 87, no. 16 (April 2013). © 2013 American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.87.165107 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society American Physical Society |
| spellingShingle | Hung, Ling-Yan Wen, Xiao-Gang Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases |
| title | Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases |
| title_full | Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases |
| title_fullStr | Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases |
| title_full_unstemmed | Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases |
| title_short | Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases |
| title_sort | quantized topological terms in weak coupling gauge theories with a global symmetry and their connection to symmetry enriched topological phases |
| url | http://hdl.handle.net/1721.1/88752 https://orcid.org/0000-0002-5874-581X |
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