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Amamodeli we-string-net athuthukisiwe nezinto ezijabulisayo zawo

Ishicilelwe kabusha nguPlato
Ishicilelwe kabusha nguPlato

Usuku:

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UDavid Green1, uPeter Huston2, Kyle Kawagoe1, UDavid Penneys1, Anup Poudel1, kanye noSean Sanford1

1I-Ohio State University
2I-Vanderbilt University

Thola leli phepha elithakazelisayo noma ufuna ukuxoxa ngalo? Scite noma shiya amazwana ku-SciRate.

abstract

Imingcele yamamodeli we-Walker-Wang isetshenziselwe ukwakha amamodeli eprojektha ahambayo aqaphela izigaba ze-chiral unitary modular tensor (UMTCs) njengezivuso zomngcele. Uma kunikezwe i-UMTC $mathcal{A}$ emele isigaba se-Witt sokudideka, isihloko [10] inikeze imodeli yeprojektha ehambayo ehlotshaniswa ne-$mathcal{A}$-enothisiwe isigaba sokuhlanganisa esingu-$mathcal{X}$ kumngcele we-2D wemodeli ye-3D Walker-Wang ehlotshaniswa ne-$mathcal{A}$. Leso sihloko sifune ukuthi okujabulisayo komngcele kunikezwe isikhungo esithuthukisiwe/i-Müger centralizer $Z^mathcal{A}(mathcal{X})$ of $mathcal{A}$ in $Z(mathcal{X})$.
Kulesi sihloko, sinikeza impatho eqinile yale modeli yomngcele we-2D, futhi siqinisekisa lokhu kugomela sisebenzisa amasu we-topological quantum field theory (TQFT), okuhlanganisa amamojula e-skein kanye ne-algebra ethile engama-semimple isigaba sayo sokumelela esichaza injabulo yomngcele. Siphinde sisebenzisa amasu e-TQFT ukukhombisa okujabulisayo kwephoyinti lenqwaba ye-3D yenqwaba ye-Walker-Wang enikezwa isikhungo se-Müger $Z_2(mathcal{A})$, futhi sakha ama-opharetha okugxuma kwenqwaba kuya komngcele $Z_2(mathcal{A })kuya ku-Z^{mathcal{A}}(mathcal{X})$ okubonisa ukuthi i-UMTC yenjabulo yomngcele $Z^{mathcal{A}}(mathcal{X})$ inokwe-symmetric-braided ehlanganiswe ngo-$Z_2( izibalo{A})$.
Lesi sihloko sihlanganisa nokubuyekezwa okuphelele okuziqukathe ngokwakho kwemodeli yenetha yentambo ye-Levin-Wen kusukela kumbono wesigaba esihlanganisiwe se-tensor, ngokuphambene nombono wophawu lwamathambo angu-$6j$.

Isithombe esifakiwe: I-$mathcal{A}$-enriched fusion isigaba $mathcal{X}$ idatha edingekayo ukuze unamathisele (2+1)D imodeli yeyunithi yezinhlamvu ye-Levin-Wen ehlotshaniswa nesigaba se-fusion $mathcal{X}$ ku-(3+1)D imodeli yentambo ye-Walker-Wang ehlotshaniswa nesigaba se-modular tensor $mathcal{A}$.

► Idatha ye-BibTeX

► Izinkomba

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Icashunwe ngu

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