Chiral de Rham Complex on Riemannian Manifolds and Special Holonomy

Springer Science and Business Media LLC - Tập 318 Số 3 - Trang 575-613 - 2013
Joel Ekstrand1, Reimundo Heluani2, Johan Kallen1, Maxim Zabzine1
1Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden
2Department of Mathematics, University of California, Berkeley, CA, 94720, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Malikov F., Schechtman V., Vaintrob A.: Chiral de Rham complex. Commun. Math. Phys. 204, 439–473 (1999)

Gorbounov V., Malikov F., Schechtman V.: Gerbes of chiral differential operators. II. Vertex algebroids. Invent. Math. 155(3), 605–680 (2004)

Ben-Zvi D., Heluani R., Szczesny M.: Supersymmetry of the chiral de Rham complex. Comp. Math. 144, 503–521 (2008)

Malikov F.: Lagrangian approach to sheaves of vertex algebras. Commun. Math. Phys. 278, 487–548 (2008)

Kapustin, A.: Chiral de Rham complex and the half-twisted sigma-model. http://arxiv.org/abs/hep-th/0504074v1 , 2005

Witten, E.: Two-dimensional models with (0,2) supersymmetry: Perturbative aspects. http://arxiv.org/abs/hep-th/0504078v3 , 2006

Frenkel E., Losev A.: Mirror symmetry in two steps: A-I-B. Commun. Math. Phys. 269, 39–86 (2007)

Frenkel, E., Losev, A., Nekrasov, N.: Instantons beyond topological theory. I. http://arxiv.org/abs/hep-th/0610149v1 , 2006

Frenkel, E., Losev, A., Nekrasov, N.: Instantons beyond topological theory. II. http://arxiv.org/abs/0803.3302v1 [hep-th], 2008

Ekstrand J., Heluani R., Källén J., Zabzine M.: Non-linear sigma models via the chiral de Rham complex. Adv. Theor. Math. Phys. 13, 1221–1254 (2009)

Heluani R.: Supersymmetry of the Chiral de Rham Complex 2: Commuting Sectors. Int. Math. Res. Notices 2009(6), 953–987 (2009)

Howe P.S., Papadopoulos G.: A Note on holonomy groups and sigma models. Phys. Lett. B263, 230–232 (1991)

Howe P.S., Papadopoulos G.: Holonomy groups and W symmetries. Commun. Math. Phys. 151, 467–480 (1993)

Odake S.: Extension of N = 2 superconformal algebra and Calabi-Yau compactification. Mod. Phys. Lett. A4, 557 (1989)

Shatashvili S.L., Vafa C.: Superstrings and manifold of exceptional holonomy. Selecta Math. 1, 347 (1995)

Heluani R., Kac V.G.: Supersymmetric vertex algebras. Commun. Math. Phys. 271, 103–178 (2007)

De Sole A., Kac V.G.: Freely generated vertex algebras and non-linear Lie conformal algebras. Commun. Math. Phys. 254(3), 659–694 (2005)

Zabzine M.: Hamiltonian perspective on generalized complex structure. Commun. Math. Phys. 263, 711–722 (2006)

Bredthauer A., Lindström U., Persson J., Zabzine M.: Generalized Kaehler geometry from supersymmetric sigma models. Lett. Math. Phys. 77, 291–308 (2006)

Zabzine M.: Lectures on generalized complex geometry and supersymmetry. Arch. Math. (Brno) 42(suppl), 119–146 (2006)

Barakat A., De Sole A., Kac V.G.: Poisson vertex algebras in the theory of Hamiltonian equations. Jpn. J. Math. 4(2), 141–252 (2009)

Joyce, D.D.: Compact manifolds with special holonomy. Oxford Mathematical Monographs. Oxford: Oxford University Press, 2000

Karigiannis S.: Flows of G 2 Structures, I. Q. J. Math. 60(4), 487–522 (2009)

Karigiannis, S.: Flows of Spin(7)-structures. In: Differential geometry and its applications. River Edge, NJ: World Scientific Publishing, 2008, pp. 263–277

Bressler P.: The first Pontryagin class. Compos. Math. 143(5), 1127–1163 (2007)

Lian B.H., Linshaw A.R.: Chiral equivariant cohomology. I. Adv. Math. 209(1), 99–161 (2007)

Lian B.H., Linshaw A.R., Song B.: Chiral equivariant cohomology. II. Trans. Amer. Math. Soc. 360(9), 4739–4776 (2008)

Grosswald, E.: Bessel polynomials, Vol. 698 of Lecture Notes in Mathematics. Berlin: Springer, 1978

Figueroa-O’Farrill J.M.: A note on the extended superconformal algebras associated with manifolds of exceptional holonomy. Phys. Lett. B392, 77–84 (1997)

Ekstrand J.: Lambda: A mathematica package for operator product expansions in vertex algebras. Comp. Phys. Commun. 182(2), 409–418 (2011)