Abstract
We find a Chern-Simons propagator on the ball with the chiral boundary condition. We use it to study perturbatively Chern-Simons boundary conditions related to 2-dim σ-models and to Poisson-Lie T-duality. In particular, we find their renormalization group flow, given by the generalized Ricci tensor. Finally we briefly discuss what happens when the Chern-Simons theory is replaced by a Courant σ-model or possibly by a more general AKSZ model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Alexandrov, A. Schwarz, O. Zaboronsky and M. Kontsevich, The Geometry of the master equation and topological quantum field theory, Int. J. Mod. Phys. A 12 (1997) 1405 [hep-th/9502010] [INSPIRE].
S. Axelrod and I.M. Singer, Chern-Simons perturbation theory. II, J. Diff. Geom. 39 (1994) 173 [hep-th/9304087] [INSPIRE].
A.L. Carey, S. Johnson, M.K. Murray, D. Stevenson and B.-L. Wang, Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories, Commun. Math. Phys. 259 (2005) 577 [math/0410013] [INSPIRE].
A.S. Cattaneo and P. Mnev, Remarks on Chern-Simons invariants, Commun. Math. Phys. 293 (2010) 803 [arXiv:0811.2045] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry I: Type II Theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].
M. Garcia-Fernandez, Ricci flow, Killing spinors, and T-duality in generalized geometry, Adv. Math. 350 (2019) 1059 [arXiv:1611.08926] [INSPIRE].
M. Gualtieri, Branes on Poisson varieties, in The Many Facets of Geometry: A Tribute to Nigel Hitchin, Oxford Science Publications, (2010).
B. Juřco and J. Vysoký, Courant algebroid connections and string effective actions, in Noncommutative geometry and physics 4, World Sci. Publ., Hackensack, NJ, U.S.A. (2017), pp. 211–265.
A. Kapustin and N. Saulina, Topological boundary conditions in abelian Chern-Simons theory, Nucl. Phys. B 845 (2011) 393 [arXiv:1008.0654] [INSPIRE].
C. Klimčík and P. Ševera, Dual nonAbelian duality and the Drinfeld double, Phys. Lett. B 351 (1995) 455 [hep-th/9502122] [INSPIRE].
M. Kontsevich, Feynman Diagrams and Low-Dimensional Topology, in Joseph A., Mignot F., Murat F., Prum B., Rentschler R. (eds) First European Congress of Mathematics Paris, July 6–10, 1992, Progress in Mathematics, vol. 120. Birkhäuser Basel.
M. Kontsevich, Deformation quantization of Poisson manifolds. 1., Lett. Math. Phys. 66 (2003) 157 [q-alg/9709040] [INSPIRE].
J. Pulmann, P. Ševera and F. Valach, A non-abelian duality for (higher) gauge theories, arXiv:1909.06151 [INSPIRE].
D. Roytenberg, AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories, Lett. Math. Phys. 79 (2007) 143 [hep-th/0608150] [INSPIRE].
M.A. Rieffel and A.S. Schwarz, Morita equivalence of multidimensional noncommutative tori, Int. J. Math. 10 (1999) 289 [math/9803057] [INSPIRE].
P. Ševera, Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory, JHEP 05 (2016) 044 [arXiv:1602.05126] [INSPIRE].
P. Ševera, Moduli spaces of flat connections and Morita equivalence of quantum tori, Doc. Math. 17 (2012) 607-625.
P. Ševera and F. Valach, Ricci flow, Courant algebroids, and renormalization of Poisson-Lie T-duality, Lett. Math. Phys. 107 (2017) 1823 [arXiv:1610.09004] [INSPIRE].
P. Ševera and F. Valach, Courant Algebroids, Poisson-Lie T-duality, and Type II Supergravities, Commun. Math. Phys. 375 (2020) 307 [arXiv:1810.07763] [INSPIRE].
K. Sfetsos, K. Siampos and D.C. Thompson, Renormalization of Lorentz non-invariant actions and manifest T-duality, Nucl. Phys. B 827 (2010) 545 [arXiv:0910.1345] [INSPIRE].
E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2009.00509
Supported in part by the NCCR SwissMAP of the Swiss National Science Foundation.
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Pulmann, J., Ševera, P. & Youmans, D.R. Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor. J. High Energ. Phys. 2020, 96 (2020). https://doi.org/10.1007/JHEP10(2020)096
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2020)096