Publications

  • Journal Papers

 

An incomplete list of my publications is summarized below in different categories. See http://arxiv.org/a/kong_l_1.html for a more complete list. 

  • The mathematical foundation of 2d open-closed rational conformal field theories based on the representation theory of vertex operator algebra:
    1. Open-string vertex algebras, categories and operads, Yi-Zhi Huang, Liang Kong, Comm. Math. Phys. 250 (2004) 433–471, [arXiv:math/0308248]
    2. Full field algebras, Yi-Zhi Huang, Liang Kong, Comm. Math. Phys. 272 (2007)345–396, [arXiv:math/0511328]
    3. Full field algebras, operads and tensor categories, Liang Kong, Adv. Math. 213 (2007) 271–340, [arXiv:math/0603065]
    4. Modular invariance for conformal full field algebras, Yi-Zhi Huang, Liang Kong, Trans.Amer. Math. Soc. 362 (2010) 3027–3067, [arXiv:math.QA/0609570]
    5. Open-closed field algebras, Liang Kong, Comm. Math. Phys., 280, 207-261 (2008) [arXiv:math.QA/0610293]
    6. Cardy condition for open-closed field algebras, Liang Kong, Comm. Math. Phys., 283, 25–92 (2008) [arXiv:math/0612255]
    7. Cardy algebras and sewing constraints, II, Liang Kong, Qin Li, Ingo Runkel, Adv. Math. 262 (2014) 604-681 [arXiv:1310.1875]

 

  • Mathematical theory of open-closed duality (or boundary-bulk duality) in 2d rational conformal field theory: 
    1. Morita classes of algebras in modular tensor categories, Liang Kong, Ingo Runkel, Adv. Math. 219, 1548–1576 (2008) [arXiv:0708.1897]
    2. Cardy algebras and sewing constraints, I, Liang Kong, Ingo Runkel, Comm. Math. Phys. 292, 871–912 (2009) [arXiv:0807.3356]
    3. Invertible defects and isomorphisms of rational CFTs, Alexei Davydov, Liang Kong, Ingo Runkel, Adv. Theor. Math. Phys., 15, (2011) 43–69 [arXiv:1004.4725]
    4. The functoriality of the centre of an algebra, Alexei Davydov, Liang Kong, Ingo Runkel, Adv. Math. 285 (2015) 811-876 [arXiv:1307.5956]

 

  • A proposal on a new representation-theoretical approach towards quantum gravity based on 2d conformal field theories:
    1. Conformal field theory and a new geometry, Liang Kong, Mathematical Foundations of Quantum Field and Perturbative String Theory, Hisham Sati, Urs Schreiber (eds.), Proceedings of Symposia in Pure Mathematics, AMS, Vol. 83 (2011) 199–244 [arXiv:1107.3649]

 

  • Lattice models of gapped edges and defects in 2d topological orders and boundary-bulk duality:
    1. Models for gapped boundaries and domain walls, Alexei Kitaev, Liang Kong, Commun. Math. Phys. 313 (2012) 351-373 [arXiv:1104.5047]
    2. Some universal properties of Levin-Wen models, Liang Kong, XVIITH International Congress of Mathematical Physics, World Scientific 444-455 (2014) [arXiv:1211.4644]
    3. The center functor is fully faithful, Liang Kong, Hao Zheng, [arXiv:1507.00503]

 

  • A mathematical theory of anyon condensation (based on many earlier results in mathematics):
    1. Anyon condensation and tensor categories, Liang Kong, Nucl. Phys. B 886 (2014) 436-482 [arXiv:1307.8244]

 

  • An application of factorization homology to the study of topological orders for the first time. Factorization homology allows explicit computation of the global observables of potentially anomalous topological orders on any stratified manifolds.
    1. Topological orders and factorization homology, Yinghua Ai, Liang Kong, Hao Zheng. THEOR. MATH. PHYS. Volume 21, Number 8, 1845–1894, 2017 [arXiv:1607.08422]

 

  • A mathematical theory of symmetry protected/enriched 2d topological orders:
    1. Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries, Tian Lan, Liang Kong, Xiao-Gang Wen, Commun. Math. Phys. 351, Issue 2, (2017) 709-739 [arXiv:1602.05936]

 

  • General categorical theory of topological orders (without symmetry) in any dimensions:
    1. Braided fusion categories, gravitational anomalies and the mathematical framework for topological orders in any dimensions, Liang Kong, Xiao-Gang Wen [arXiv:1405.5858]
    2. Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers, Liang Kong, Xiao-Gang Wen, Hao Zheng, [arXiv:1502.01690]
    3. Boundary-bulk relation in topological orders, Liang Kong, Xiao-Gang Wen, Hao Zheng, Phys. B 922 (2017), 62--76 [arXiv:1702.00673]

 

  • A unified mathematical theory of gapped/gapless edges of 2d topological orders:
    1. Drinfeld center of enriched monoidal categories, Liang Kong, Hao Zheng, Advances in Mathematics 323 (2018) 411-426 [arXiv:1704.01447]
    2. Gapless edges of 2d topological orders and enriched monoidal categories, Liang Kong, Hao Zheng, Phys. B 927 (2018) 140--165 [arXiv:1705.01087]
    3. A mathematical theory of gapless edges of 2d topological orders I, Liang Kong, Hao Zheng, Journal of High Energy Physics, to appear [arXiv:1905.04924]
    4. A mathematical theory of gapless edges of 2d topological orders II, Liang Kong, Hao Zheng, [arXiv:1912.01760]
    5. A topological phase transition on the edge of the 2d 2 topological order, Wei-Qiang Chen, Chao-Ming Jian, Liang Kong, Yi-Zhuang You, Hao Zheng, [arXiv:1903.12334]

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