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Published online by Cambridge University Press:  10 September 2021

Kevin Costello
Affiliation:
Perimeter Institute for Theoretical Physics, Waterloo, Ontario
Owen Gwilliam
Affiliation:
University of Massachusetts, Amherst
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References

Alexandrov, M., Kontsevich, M., Schwarz, A., and Zaboronsky, O. 1997. The geometry of the master equation and topological field theory. Internat. J. Modern Phys., 12(7), 14051429.Google Scholar
Atiyah, M. F., Hitchin, N. J., and Singer, I. M. 1978. Self-duality in four-dimensional Riemannian geometry. Proc. Roy. Soc. London Ser. A, 362(1711), 425461.Google Scholar
Axelrod, S., and Singer, I. M. 1992. Chern-Simons perturbation theory. Pages 345 of: Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991). World Scientific Publishing, River Edge, NJ.Google Scholar
Axelrod, S., and Singer, I. M. 1994. Chern-Simons perturbation theory. II. J. Differential Geom., 39(1), 173213.Google Scholar
Baez, J. C. 1996. Four-dimensional BF theory as a topological quantum field theory. Lett. Math. Phys., 38(2), 129143.Google Scholar
Baez, J. C., and Crans, A. S. 2004. Higher-dimensional algebra. VI. Lie 2-algebras. Theory Appl. Categ., 12, 492538.Google Scholar
Baez, J. C., and Rogers, C. L. 2010. Categorifiedsymplectic geometry and the string Lie 2-algebra. Homology Homotopy Appl., 12(1), 221236.Google Scholar
Bashkirov, D., and Voronov, A. A. 2017. The BV formalism for L-algebras. J. HomotopyRelat. Struct., 12(2), 305327.Google Scholar
Beem, C., Ben-Zvi, D., Bullimore, M., Dimofte, T., and Neitzke, A. 2020. Secondary products in supersymmetric field theory. Ann. Henri Poincaré, 21(4), 12351310.Google Scholar
Ben-Bassat, O., Brav, C., Bussi, V., and Joyce, D. 2015. A ‘Darboux theorem’ for shifted symplectic structures on derived Artin stacks, with applications. Geom. Topol., 19(3), 12871359.Google Scholar
Benini, M., Perin, M., and Schenkel, A. 2020. Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds. Comm. Math. Phys., 377(2), 971997.Google Scholar
Benini, M., Schenkel, A., and Woike, L. 2019. Homotopy theory of algebraic quantum field theories. Lett. Math. Phys., 109(7), 14871532.Google Scholar
Berline, N., Getzler, E., and Vergne, M. 1992. Heat kernels and Dirac operators. Grundlehren der MathematischenWissenschaften [Fundamental Principles of Mathematical Sciences], vol. 298. Springer-Verlag, Berlin.Google Scholar
Braun, C., and Lazarev, A. 2013. Homotopy BV algebras in Poisson geometry. Trans. Moscow Math. Soc., 217227.Google Scholar
Brav, C., Bussi, V., and Joyce, D. 2019. A Darboux theorem for derived schemes with shifted symplectic structure. J. Amer. Math. Soc., 32(2), 399443.Google Scholar
Calaque, D., Pantev, T., Toën, B., Vaquié, M., and Vezzosi, G. 2017. Shifted Poisson structures and deformation quantization. J. Topol., 10(2), 483584.Google Scholar
Cattaneo, A. S., Cotta-Ramusino, P., Fucito, F., Martellini, M., Rinaldi, M., Tanzini, A., and Zeni, M. 1998. Four-dimensional Yang-Mills theory as a deformation of topological BF theory. Comm. Math. Phys., 197(3), 571621.Google Scholar
Cattaneo, A. S., Felder, G., and Tomassini, L. 2002. Fedosov connections on jet bundles and deformation quantization. Pages 191202 of: Deformation quantization (Strasbourg, 2001). IRMA Lectures in Mathematics and Theoretical Physics, vol. 1. deGruyter, Berlin.Google Scholar
Cattaneo, A. S., and Rossi, C. A. 2001. Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: the BV action and generalized Wilson loops. Comm. Math. Phys., 221(3), 591657.Google Scholar
Costello, K. n.d. M-theory in the Omega-background and 5-dimensional non-commutative gauge theory. Available at www.arxiv.org/abs/1610. 04144.Google Scholar
Costello, K. 2007. Renormalisation and the Batalin-Vilkovisky formalism. Available at www.arxiv.org/abs/0706.1533.Google Scholar
Costello, K. 2010. A geometric construction of the Witten genus, I. In: Proceedings of the International Congress of Mathematicians (Hyderabad, 2010).Google Scholar
Costello, K. 2011a. A geometric construction of the Witten genus, II. Available at www.arxiv.org/abs/1112.0816.Google Scholar
Costello, K. 2011b. Renormalization and effective field theory. Mathematical Surveys and Monographs, vol. 170. American Mathematical Society, Providence, RI.Google Scholar
Costello, K. 2013a. Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4. Pure Appl. Math. Q., 9(1), 73165.Google Scholar
Costello, K. 2013b. Supersymmetric gauge theory and the Yangian. Available at www.arxiv.org/abs/1303.2632.Google Scholar
Costello, K. 2017. Holography and Koszul duality: the example of the M2 brane. Available at www.arxiv.org/abs/1705.02500.Google Scholar
Costello, K., Witten, E., and Yamazaki, M. 2019. Gauge theory and integrability, I. Pages 17151 of: Proceedings of the Seventh International Congress of Chinese Mathematicians, Vol. I. Advanced Lectures in Mathematics (ALM), vol. 43. International Press, Somerville, MA.Google Scholar
Eisenbud, D., and Harris, J. 2000. The geometry of schemes. Graduate Texts in Mathematics, vol. 197. Springer-Verlag, New York.Google Scholar
Elliott, C., Williams, B., and Yoo, P. 2018. Asymptotic freedom in the BV formalism. J. Geom. Phys., 123, 246283.Google Scholar
Fantechi, B., Göttsche, L., Illusie, L., Kleiman, S. L., Nitsure, N., and Vistoli, A. 2005. Fundamental algebraic geometry: Grothendieck's FGA explained. Mathematical Surveys and Monographs, vol. 123. American Mathematical Society, Providence, RI.Google Scholar
Fløystad, G. 2006. Koszul duality and equivalences of categories. Trans. Amer. Math. Soc., 358(6), 23732398.Google Scholar
Frenkel, E., and Ben-Zvi, D. 2004. Vertex algebras and algebraic curves. Second edn. Mathematical Surveys and Monographs, vol. 88. American Mathematical Society, Providence, RI.Google Scholar
Gaiotto, D., and Oh, J. 2019. Aspects of -deformed M-theory. Available at www.arxiv.org/abs/1907.06495.Google Scholar
Getzler, E. 2009. Lie theory for nilpotent L-algebras. Ann. of Math. (2), 170(1), 271301.Google Scholar
Gilkey, P. B. 1995. Invariance theory, the heat equation, and the Atiyah-Singer index theorem. Second edn. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL.Google Scholar
Gould, H. W., and Shonhiwa, T. 2008. A catalog of interesting Dirichlet series. Missouri J. Math. Sci., 20(1), 117.Google Scholar
Grady, R., and Gwilliam, O. 2015. L spaces and derived loop spaces. New York J. Math., 21, 231272.Google Scholar
Grady, R. E., Li, Q., and Li, S. 2017. Batalin-Vilkovisky quantization and the algebraic index. Adv. Math., 317, 575639.Google Scholar
Guay, N. 2007. Affine Yangians and deformed double current algebras in type A. Adv. Math., 211(2), 436484.Google Scholar
Guay, N, and Yang, Y. 2017. On deformed double current algebras for simple Lie algebras. Math. Res. Lett., 24(5), 13071384.Google Scholar
Gwilliam, O., Gorbounov, V., and Williams, B. 2020. Chiral differential operators via quantization of the holomorphic σ -model. Astérisque, 419. Available at www.arxiv.org/abs/1610.09657.Google Scholar
Gwilliam, O., and Grady, R. 2014. One-dimensional Chern-Simons theory and the  genus. Algebr. Geom. Topol., 14(4), 22992377.Google Scholar
Gwilliam, O., and Haugseng, R. 2018. Linear Batalin-Vilkovisky quantization as a functor of ∞-categories. Selecta Math. (N.S.), 24(2), 12471313.Google Scholar
Gwilliam, O., and Williams, B. R. 2021. Higher Kac-Moody algebras and symmetries of holomorphic field theories. Adv. Theor. Math. Phys., 25(1).Google Scholar
Henneaux, M., and Teitelboim, C. 1992. Quantization of gauge systems. Princeton University Press, Princeton, NJ.Google Scholar
Henriques, A. 2008. Integrating L-algebras. Compos. Math., 144(4), 10171045.Google Scholar
Hernandez, D. 2009. Quantum toroidal algebras and their representations. Selecta Math. (N.S.), 14(3–4), 701725.Google Scholar
Hinich, V. 2001. DG coalgebras as formal stacks. J. Pure Appl. Algebra, 162(2–3), 209250.Google Scholar
Hohm, O., and Zwiebach, B. 2017. L algebras and field theory. Fortschr. Phys., 65(3–4), 1700014, 33.Google Scholar
Joyce, D. 2015. A classical model for derived critical loci. J. Differential Geom., 101(2), 289367.Google Scholar
Jurčo, B., Macrelli, T., Raspollini, L., Sämann, C., and Wolf, M. 2019b. L-algebras, the BV formalism, and classical fields. Fortschr. Phys., 67(8–9, Special issue: Proceedings of the LMS/EPSRC Durham Symposium on Higher Structures in M-Theory), 1910025, 17.Google Scholar
Jurčo, B., Raspollini, L., Sämann, C., and Wolf, M. 2019a. L-algebras of classical field theories and the Batalin-Vilkovisky formalism. Fortschr. Phys., 67(7), 1900025, 60.Google Scholar
Kapranov, M., Kontsevich, M., and Soibelman, Y. 2016. Algebra of the infrared and secondary polytopes. Adv. Math., 300, 616671.Google Scholar
Kapustin, A., and Witten, E. 2007. Electric-magnetic duality and the geometric Langlands program. Commun. Number Theory Phys., 1(1), 1236.Google Scholar
Keller, B. 2006. A-infinity algebras, modules and functor categories. Pages 6793 of: Trends in representation theory of algebras and related topics. Contemporary Mathematics, vol. 406. American Mathematical Society, Providence, RI.Google Scholar
Knudsen, B. 2018. Higher enveloping algebras. Geom. Topol., 22(7), 40134066.Google Scholar
Kontsevich, M. 1993. Formal (non)commutative symplectic geometry. Pages 173187 of: The Gelfand Mathematical Seminars, 1990–1992. Birkhäuser, Boston, MA.Google Scholar
Kontsevich, M. 1994. Feynman diagrams and low-dimensional topology. Pages 97121 of: First European Congress of Mathematics, Vol. II (Paris, 1992). Progress in Mathematics, vol. 120. Birkhäuser, Basel.Google Scholar
Kontsevich, M. 2003. Deformation quantization of Poisson manifolds. Lett. Math. Phys., 66(3), 157216.Google Scholar
Kontsevich, M, and Soibelman, Y. n.d. Deformation theory, volume I. Available at www.math.ksu.edu/∼soibel/.Google Scholar
Kontsevich, M., and Soibelman, Y. 2009. Notes on A-algebras, A-categories and non-commutative geometry. Pages 153219 of: Homological mirror symmetry. Lecture Notes in Physics, vol. 757. Springer, Berlin.Google Scholar
Koszul, J.-L. 1985. Crochet de Schouten-Nijenhuis etcohomologie. Pages 257271 of: ElieCartanet les mathematiquesd’aujourd’hui. Asterisque.Google Scholar
Li, Q., and Li, S. 2016. On the B-twisted topological sigma model and Calabi–Yau geometry. J. Differential Geom., 102(3), 409484.Google Scholar
Li, S. 2012. Feynman graph integrals and almost modular forms. Commun. Number Theory Phys., 6(1), 129157.Google Scholar
Lurie, J. n.d. Spectral Algebraic Geometry. Available at www.math.ias.edu/∼lurie/papers/SAG-rootfile.pdf.Google Scholar
Lurie, J. 2010. Moduli problems for ring spectra. Pages 10991125 of: Proceedings of the International Congress of Mathematicians. Volume II. Hindustan Book Agency, New Delhi.Google Scholar
Manetti, M. 2009. Differential graded Lie algebras and formal deformation theory. Pages 785810 of: Algebraic geometry—Seattle 2005. Part 2. Proceedings of Symposia in Pure Mathematics, vol. 80. American Mathematical Society, Providence, RI.Google Scholar
Maulik, D., and Okounkov, A. 2019. Quantum groups and quantum cohomology. Astérisque, ix+209.Google Scholar
Melani, V., and Safronov, P. 2018a. Derived coisotropic structures I: affine case. Selecta Math. (N.S.), 24(4), 30613118.Google Scholar
Melani, V., and Safronov, P. 2018b. Derived coisotropic structures II: stacks and quantization. Selecta Math. (N.S.), 24(4), 31193173.Google Scholar
Nekrasov, N. 2005. Lectures on curved beta-gamma systems, pure spinors, and anomalies. Available at www.arxiv.org/abs/hep-th/0511008.Google Scholar
Pantev, T., Toën, B., Vaquié, M., and Vezzosi, G. 2013. Shifted symplectic structures. Publ. Math. Inst. HautesÉtudes Sci., 117, 271328.Google Scholar
Patodi, V. K. 1971. An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds. J. Differential Geom., 5, 251283.Google Scholar
Polishchuk, A., and Positselski, L. 2005. Quadratic algebras. University Lecture Series, vol. 37. American Mathematical Society, Providence, RI.Google Scholar
Positselski, L. E. 1993. Nonhomogeneous quadratic duality and curvature. Funktsional. Anal. iPrilozhen., 27(3), 5766, 96.Google Scholar
Pridham, J. P. 2010. Unifying derived deformation theories. Adv. Math., 224(3), 772826.Google Scholar
Pridham, J. P. 2017. Shifted Poisson and symplectic structures on derived N-stacks. J. Topol., 10(1), 178210.Google Scholar
Pridham, J. P. 2019. Deformation quantisation for (−1)-shifted symplectic structures and vanishing cycles. Algebr. Geom., 6(6), 747779.Google Scholar
Quillen, D. 1969. Rational homotopy theory. Ann. of Math. (2), 90, 205295.Google Scholar
Rabinovich, E. 2019. A mathematical analysis of the axial anomaly. Lett. Math. Phys., 109(5), 10551117.Google Scholar
Rabinovich, E. 2020. The Batalin-Vilkovisky formalism and the determinant line bundle. J. Geom. Phys., 156, 103792, 18.Google Scholar
Rejzner, K. 2016. Perturbative algebraic quantum field theory: An introduction for mathematicians. Mathematical Physics Studies. Springer, Cham.Google Scholar
Rozenblyum, N. 2015. Symplecticgroupoids and shifted Poisson structures. Talk at Warwick EPSRC Symposium on Derived Algebraic Geometry, with a Focus on Derived Symplectic Techniques. University of Warwick.Google Scholar
Saberi, I., and Williams, B. R. 2019. Superconformal algebras and holomorphic field theories. Available at www.arxiv.org/abs/1910.04120.Google Scholar
Saberi, I., and Williams, B. R. 2020. Twisted characters and holomorphic symmetries. Lett. Math. Phys., 110(10), 27792853.Google Scholar
Safronov, P. 2017. Poisson reduction as a coisotropic intersection. High. Struct., 1(1), 87121.Google Scholar
Safronov, P. 2018. Braces and Poisson additivity. Compos. Math., 154(8), 16981745.Google Scholar
Scheimbauer, C. 2014. On fully extended topological field theories. Ph.D. thesis at ETH Zurich.Google Scholar
Schiffmann, O., and Vasserot, E. 2013. Cherednik algebras, W-algebras and the equivariantcohomology of the moduli space of instantons on A2. Publ. Math. Inst. HautesÉtudes Sci., 118, 213342.Google Scholar
Schwarz, A. 1993. Geometry of Batalin-Vilkovisky quantization. Comm. Math. Phys., 155(2), 249260.Google Scholar
Tarkhanov, N. N. 1995. Complexes of differential operators. Mathematics and Its Applications, vol. 340. Kluwer Academic Publishers Group, Dordrecht. Translated from the 1990 Russian original by P. M. Gauthier and revised by the author.Google Scholar
Toën, B. 2009. Higher and derived stacks: a global overview. Pages 435487 of: Algebraic geometry—Seattle 2005. Part 1. Proceedings of Symposia in Pure Mathematics, vol. 80. American Mathematical Society, Providence, RI.Google Scholar
Toën, B. 2014. Derived algebraic geometry and deformation quantization. Pages 769792 of: Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. II. Kyung Moon Sa, Seoul.Google Scholar
Vafa, C., and Witten, E. 1994. A strong coupling test of S-duality. Nuclear Phys. B, 431(1–2), 377.Google Scholar
Vezzosi, G. 2020. Basic structures on derived critical loci. Differential Geom. Appl., 71, 101635, 11.Google Scholar
Williams, B. 2017. The Virasoro vertex algebra and factorization algebras on Riemann surfaces. Lett. Math. Phys., 107(12), 21892237.Google Scholar
Williams, B. R. 2020. Renormalization for holomorphic field theories. Comm. Math. Phys., 374(3), 16931742.Google Scholar
Witten, E. 2007. Two-dimensional models with (0,2)supersymmetry: perturbative aspects. Adv. Theor. Math. Phys., 11(1), 163.Google Scholar

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  • References
  • Kevin Costello, Owen Gwilliam, University of Massachusetts, Amherst
  • Book: Factorization Algebras in Quantum Field Theory
  • Online publication: 10 September 2021
  • Chapter DOI: https://doi.org/10.1017/9781316678664.021
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  • References
  • Kevin Costello, Owen Gwilliam, University of Massachusetts, Amherst
  • Book: Factorization Algebras in Quantum Field Theory
  • Online publication: 10 September 2021
  • Chapter DOI: https://doi.org/10.1017/9781316678664.021
Available formats
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  • References
  • Kevin Costello, Owen Gwilliam, University of Massachusetts, Amherst
  • Book: Factorization Algebras in Quantum Field Theory
  • Online publication: 10 September 2021
  • Chapter DOI: https://doi.org/10.1017/9781316678664.021
Available formats
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