Perturbative path-integral of string fields and the A∞ structure of the BV master equation
The perturbative path-integral gives a morphism of the (quantum) A∞ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the Batalin–Vilkovisky (BV) formalism, any effective action also solves the BV master equation,...
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| Published in | Progress of theoretical and experimental physics Vol. 2022; no. 11 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Oxford University Press
01.11.2022
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| Online Access | Get full text |
| ISSN | 2050-3911 2050-3911 |
| DOI | 10.1093/ptep/ptac132 |
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| Abstract | The perturbative path-integral gives a morphism of the (quantum) A∞ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the Batalin–Vilkovisky (BV) formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a quantum A∞ structure, the path-integral preserves this intrinsic A∞ structure of quantum field theory, where A∞ reduces to L∞ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string-field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite α′, reduction of gauge and unphysical degrees, the S-matrix, and gauge-invariant observables. |
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| AbstractList | The perturbative path-integral gives a morphism of the (quantum) A∞ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the Batalin–Vilkovisky (BV) formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a quantum A∞ structure, the path-integral preserves this intrinsic A∞ structure of quantum field theory, where A∞ reduces to L∞ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string-field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite α′, reduction of gauge and unphysical degrees, the S-matrix, and gauge-invariant observables. The perturbative path-integral gives a morphism of the (quantum) A∞ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the Batalin–Vilkovisky (BV) formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a quantum A∞ structure, the path-integral preserves this intrinsic A∞ structure of quantum field theory, where A∞ reduces to L∞ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string-field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite α′, reduction of gauge and unphysical degrees, the S-matrix, and gauge-invariant observables. |
| Author | Masuda, Toru Matsunaga, Hiroaki |
| Author_xml | – sequence: 1 givenname: Toru surname: Masuda fullname: Masuda, Toru – sequence: 2 givenname: Hiroaki surname: Matsunaga fullname: Matsunaga, Hiroaki email: hiroaki.matsunaga@omu.ac.jp |
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| Cites_doi | 10.1103/PhysRevD.100.045017 10.1007/s11005-015-0791-9 10.1007/JHEP11(2021)208 10.1142/S0129055X07002912 10.1016/0370-2693(81)90205-7 10.1016/0550-3213(86)90155-0 10.1088/1126-6708/2008/03/050 10.1088/1126-6708/2009/10/066 10.1007/JHEP01(2017)108 10.1007/JHEP10(2017)057 10.1007/s00220-014-2027-8 10.1088/1126-6708/2008/07/063 10.1515/9780691213866 10.1088/1126-6708/2004/04/070 10.1007/JHEP05(2017)095 10.4310/ATMP.2006.v10.n4.a1 10.1007/JHEP05(2018)020 10.1016/0550-3213(83)90680-6 10.1063/1.5022890 10.1007/JHEP03(2012)012 10.1007/JHEP11(2015)187 10.1007/BF02097392 10.1090/conm/718/14479 10.1007/JHEP04(2019)143 10.1007/PL00005575 10.1088/1126-6708/2001/07/016 10.1016/0550-3213(93)90388-6 10.1002/prop.201900025 10.1093/ptep/ptab159 10.1016/S0550-3213(02)00495-9 10.1007/JHEP10(2019)119 10.1142/S0217751X97001031 10.1007/s00220-012-1654-1 10.1007/JHEP07(2019)115 10.1088/1126-6708/1999/12/027 10.1007/s11005-013-0615-8 |
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| Title | Perturbative path-integral of string fields and the A∞ structure of the BV master equation |
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