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Lecture notes on conformal field theory

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arxiv 2501.06616 v2 pith:5F5RN2XU submitted 2025-01-11 math-ph hep-thmath.MP

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These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and expanded in coauthorship with Nicolai Reshetikhin.

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48 extracted references · 44 canonical work pages

  1. [1]

    Introduction to the variational bicomp lex

    I. M. Anderson, “Introduction to the variational bicomp lex.” (1992)

  2. [2]

    Geometric quant ization of Chern-Simons gauge theory,

    S. Axelrod, S. Della Pietra, E. Witten, “Geometric quant ization of Chern-Simons gauge theory,” J. Diff. Geom. 33.3 (1991) 787–902

  3. [3]

    Topological quantum field theory

    M. Atiyah, “Topological quantum field theory.” Publicat ions Math´ ematiques de l’IH´ES 68 (1988) 175–186

  4. [4]

    Topological Lagrangians and coho mology

    M. Atiyah, L. Jeffrey, “Topological Lagrangians and coho mology.” Journal of Geometry and Physics 7.1 (1990) 119–136

  5. [5]

    Frobenius manifolds and formality of Lie algebras of polyvector fields,

    S. Barannikov, M. Kontsevich, “Frobenius manifolds and formality of Lie algebras of polyvector fields,” Internat. Math. Res. Notes 14(1998), 20 1–215

  6. [6]

    Infin ite conformal symmetry in two-dimensional quantum field theory,

    A. A. Belavin, A. M. Polyakov, A. B. Zamolodchikov, “Infin ite conformal symmetry in two-dimensional quantum field theory,” Nuclear Physics B 24 1.2 (1984) 333–380

  7. [7]

    Perturbative q uantum gauge theories on manifolds with boundary

    A. S. Cattaneo, P. Mnev, N. Reshetikhin, “Perturbative q uantum gauge theories on manifolds with boundary.” Communications in Mathematical Physics 357, no. 2 (2018) 631–730

  8. [8]

    Lectures on symplectic geometry,

    A. Cannas Da Silva, “Lectures on symplectic geometry,” V ol. 3575. Berlin: Springer (2008)

Show all 48 references
  1. [9]

    Conformal field theory

    P. Di Francesco, P. Mathieu, D. S´ en´ echal, “Conformal field theory.” Springer Science & Business Media, 2012

  2. [10]

    Integrable systems in topological field t heory

    B. Dubrovin, “Integrable systems in topological field t heory.” Nucl. Phys. B379 (1992) 627–689

  3. [11]

    Geometry of 2D topological field theories

    B. Dubrovin, “Geometry of 2D topological field theories .” In: Springer LNM, 1620 (1996) 120–348

  4. [12]

    A primer on mapping class groups,

    B. Farb, D. Margalit. “A primer on mapping class groups, ” Princeton university press (2011)

  5. [13]

    Verma modules over the Viraso ro algebra

    B. L. Feigin, D. B. Fuchs, “Verma modules over the Viraso ro algebra.” Topology. Springer, Berlin, Heidelberg (1984) 230–245. 297 BIBLIOGRAPHY 298

  6. [14]

    Mirror symmetry in two steps: A–I –B,

    E. Frenkel, A. Losev, “Mirror symmetry in two steps: A–I –B,” Communications in mathematical physics 269.1 (2007) 39–86

  7. [15]

    The Chern-Simons theory and kno t polynomials,

    J. Fr¨ ohlich, C. King, “The Chern-Simons theory and kno t polynomials,” Communica- tions in mathematical physics 126.1 (1989) 167–199

  8. [16]

    Lectures on conformal field theory

    K. Gawedzki, “Lectures on conformal field theory.” No. I HES-P-97-02. SCAN-9703129, 1997

  9. [17]

    SU(2) Chern-Simons theory at genus zero,

    K. Gawedzki, A. Kupiainen, “SU(2) Chern-Simons theory at genus zero,” Communica- tions in mathematical physics 135.3 (1991) 531–546

  10. [18]

    Batalin-Vilkovisky algebras and two-dim ensional topological field theories,

    E. Getzler, "Batalin-Vilkovisky algebras and two-dim ensional topological field theories," Communications in mathematical physics 159.2 (1994) 265–2 85

  11. [19]

    Applied conformal field theory,

    P. Ginsparg, “Applied conformal field theory,” arXiv pr eprint hep-th/9108028 (1988)

  12. [20]

    Two-dimensional Yang-Mills theory on surfaces with corners in Batalin–Vilkovisky formalism

    R. Iraso, P. Mnev, “Two-dimensional Yang-Mills theory on surfaces with corners in Batalin–Vilkovisky formalism.” Communications in Mathem atical Physics 370, no. 2 (2019) 637–702

  13. [21]

    Feynman-diagrammatic descripti on of the asymptotics of the time evolution operator in quantum mechanics

    Th. Johnson-Freyd, “Feynman-diagrammatic descripti on of the asymptotics of the time evolution operator in quantum mechanics.” Letters in Mathe matical Physics 94, no. 2 (2010) 123–149

  14. [22]

    Highest weight representations of infinite d imensional Lie algebras

    V. G. Kac, "Highest weight representations of infinite d imensional Lie algebras", Proc. Internat. Congress Mathematicians (Helsinki, 1978)

  15. [23]

    Bombay lectures on highest weigh t representations of infinite dimensional Lie algebras

    V. G. Kac, A. K. Raina, “Bombay lectures on highest weigh t representations of infinite dimensional Lie algebras.” World scientific, 1987

  16. [24]

    Two-dimensional pertur bative scalar QFT and Atiyah- Segal gluing

    S. Kandel, P. Mnev, K. Wernli, “Two-dimensional pertur bative scalar QFT and Atiyah- Segal gluing.” arXiv preprint arXiv:1912.11202 (2019)

  17. [25]

    Intersection theory of moduli space of stable N-pointed curves of genus zero,

    S. Keel, “Intersection theory of moduli space of stable N-pointed curves of genus zero,” Trans. AMS 330.2 (1992) 545–574

  18. [26]

    Current Algebra a nd Wess–Zumino Model in Two-Dimensions,

    V. G. Knizhnik, A. B. Zamolodchikov, “Current Algebra a nd Wess–Zumino Model in Two-Dimensions,” Nucl. Phys. B, 247.1 (1984) 83–103

  19. [27]

    Conformal field theory and topology

    T. Kohno, “Conformal field theory and topology.” Americ an Mathematical Soc., 2002

  20. [28]

    Gromov-Witten classes, qua ntum cohomology, and enu- merative geometry,

    M. Kontsevich, Yu. Manin, “Gromov-Witten classes, qua ntum cohomology, and enu- merative geometry,” Commun. Math. Phys. 164 (1994) 525–562

  21. [29]

    A. S. Losev, Lectures on topological quantum field theor y, 2008 (lectures given online in Russian). BIBLIOGRAPHY 299

  22. [30]

    TQFT, homological algebra and elements of K. Saito’s theory of Primitive form: an attempt of mathematical text written by mathematic al physicist

    A. S. Losev, “TQFT, homological algebra and elements of K. Saito’s theory of Primitive form: an attempt of mathematical text written by mathematic al physicist.” In: Primi- tive Forms and Related Subjects–Kavli IPMU 2014, vol. 83, pp . 269–294. Mathematical Society of Japan, 2019

  23. [31]

    Two-dimensional ab elian BF theory in Lorenz gauge as a twisted N=(2, 2) superconformal field theory,

    A. S. Losev, P. Mnev, D. R. Youmans, "Two-dimensional ab elian BF theory in Lorenz gauge as a twisted N=(2, 2) superconformal field theory," Jou rnal of Geometry and Physics 131 (2018) 122–137

  24. [32]

    Two-dimensional no n-abelian BF theory in Lorenz gauge as a solvable logarithmic TCFT,

    A. S. Losev, P. Mnev, D. R. Youmans, "Two-dimensional no n-abelian BF theory in Lorenz gauge as a solvable logarithmic TCFT," Communicatio ns in Mathematical Physics 376.2 (2020) 993–1052

  25. [33]

    Superconnections, Thom classe s, and equivariant differential forms,

    V. Mathai, D. Quillen, “Superconnections, Thom classe s, and equivariant differential forms,” Topology, 25.1 (1986) 85–110

  26. [34]

    Crystal statistics. I. A two-dimensional model with an order-disorder tran- sition,

    L. Onsager, “Crystal statistics. I. A two-dimensional model with an order-disorder tran- sition,” Physical Review, Series II, 65 (3–4) (1944) 117–14 9

  27. [35]

    Decorated Teichm¨ uller theory

    R. C. Penner, “Decorated Teichm¨ uller theory.” Vol. 1. European Mathematical Society, 2012

  28. [36]

    Lectures on quantization of gauge sys tems,

    N. Reshetikhin, “Lectures on quantization of gauge sys tems,” In: New Paths Towards Quantum Gravity. Springer, Berlin, Heidelberg (2010) 125–190

  29. [37]

    A mathematical introduction to con formal field theory

    M. Schottenloher, “A mathematical introduction to con formal field theory.” Vol. 759. Springer (2008)

  30. [38]

    The definition of conformal field theory,

    G. Segal, “The definition of conformal field theory,” Diff erential geometrical methods in theoretical physics. Springer, Dordrecht (1988) 165–171

  31. [39]

    A field theory of currents,

    H. Sugawara, “A field theory of currents,” Phys. Rev. 170 , 1659 (1968)

  32. [40]

    Fusion rules and modular transformation s in 2D conformal field theory,

    E. Verlinde, “Fusion rules and modular transformation s in 2D conformal field theory,” Nuclear Physics B, 300.3 (1988) 360–376

  33. [41]

    Topological conformal field theories fr om gauge-fixed topological gauge theories: a case study,

    D. R. Youmans, “Topological conformal field theories fr om gauge-fixed topological gauge theories: a case study,” Ph.D. dissertation, Universit´ e d e Gen` eve (2020)

  34. [42]

    Supersymmetry and Morse theory,

    E. Witten, “Supersymmetry and Morse theory,” Journal o f differential geometry 17.4 (1982) 661–692

  35. [43]

    Topological sigma models,

    E. Witten, “Topological sigma models,” Commun. Math. P hys. 118 (1988) 411–449

  36. [44]

    Topological quantum field theory,

    E. Witten, “Topological quantum field theory,” Comm. Ma th. Phys. Volume 117, Num- ber 3 (1988) 353–386

  37. [45]

    Quantum field theory and the Jones polynomia l

    E. Witten, “Quantum field theory and the Jones polynomia l.” Communications in Math- ematical Physics 121.3 (1989) 351–399. BIBLIOGRAPHY 300

  38. [46]

    Two-dimensional gravity and intersection theory on moduli space

    E. Witten, “Two-dimensional gravity and intersection theory on moduli space.” Surveys in Diff. Geom. 1 (1991) 243–310

  39. [47]

    Mirror manifolds and topological field theo ry

    E. Witten, “Mirror manifolds and topological field theo ry.” arXiv:hep-th/9112056 (1991)

  40. [48]

    Superstring perturbation theory revisite d,

    E. Witten, “Superstring perturbation theory revisite d,” arXiv:1209.5461 (2012)

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