Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
modular operads; connected sum; Batalin-Vilkovisky algebra; homological perturbation lemma
modular operads; connected sum; Batalin-Vilkovisky algebra; homological perturbation lemma
Summary:
We introduce the connected sum for modular operads. This gives us a graded commutative associative product, and together with the BV bracket and the BV Laplacian obtained from the operadic composition and self-composition, we construct the full Batalin-Vilkovisky algebra. The BV Laplacian is then used as a perturbation of the special deformation retract of formal functions to construct a minimal model and compute an effective action.
References:
[1] Barannikov, S.: Modular operads and Batalin-Vilkovisky geometry. Int. Math. Res. Not. IMRN 19 (2007), 31 pp., Art. ID rnm075. MR 2359547
[2] Chuang, J., Lazarev, A.: Abstract Hodge decomposition and minimal models for cyclic algebras. Lett. Math. Phys. 89 (1) (2009), 33–49. DOI 10.1007/s11005-009-0314-7 | MR 2520178
[3] Doubek, M., Jurčo, B., Münster, K.: Modular operads and the quantum open-closed homotopy algebra. J. High Energy Phys. 158 (12) (2015), 54 pp., Article ID 158. MR 3464644
[4] Doubek, M., Jurčo, B., Peksová, L., Pulmann, J.: Quantum homotopy algebras. in preparation.
[5] Doubek, M., Jurčo, B., Pulmann, J.: Quantum $L_\infty $ algebras and the homological perturbation lemma. Comm. Math. Phys. 367 (1) (2019), 215–240. DOI 10.1007/s00220-019-03375-x | MR 3933409
[6] Eilenberg, S., MacLane, S.: On the groups $H(\Pi , n)$. I. Ann. of Math. (2) 58 (1) (1953), 55–106. MR 0056295
[7] Markl, M.: Loop homotopy algebras in closed string field theory. Comm. Math. Phys. 221 (2) (2001), 367–384. DOI 10.1007/PL00005575 | MR 1845329
[8] Schwarz, A.: Geometry of Batalin-Vilkovisky quantization. Comm. Math. Phys. 155 (2) (1993), 249–260. DOI 10.1007/BF02097392 | MR 1230027 | Zbl 0786.58017
[9] Zwiebach, B.: Oriented open-closed string theory revisited. Ann. Physics 267 (2) (1998), 193–248. DOI 10.1006/aphy.1998.5803 | MR 1638333
Search
Partner of
