L∞-Algebras, the BV Formalism, and Classical Fields

Branislav Jurčo, Tommaso Macrelli, Lorenzo Raspollini, Christian Saemann, Martin Wolf

Research output: Contribution to conferencePaper

Abstract

We summarise some of our recent works on L∞-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of L∞-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of L∞-quasi-isomorphisms, and we propose a twistor space action.
Original languageEnglish
Publication statusAccepted/In press - 7 Mar 2019
EventLondon Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory - Durham, United Kingdom
Duration: 12 Aug 201818 Aug 2018

Seminar

SeminarLondon Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory
CountryUnited Kingdom
CityDurham
Period12/08/1818/08/18

Fingerprint

gauge theory
algebra
formalism
isomorphism
lightning
Yang-Mills theory
bundles

Keywords

  • hep-th

Cite this

Jurčo, B., Macrelli, T., Raspollini, L., Saemann, C., & Wolf, M. (Accepted/In press). L∞-Algebras, the BV Formalism, and Classical Fields. Paper presented at London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory, Durham, United Kingdom.
Jurčo, Branislav ; Macrelli, Tommaso ; Raspollini, Lorenzo ; Saemann, Christian ; Wolf, Martin. / L∞-Algebras, the BV Formalism, and Classical Fields. Paper presented at London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory, Durham, United Kingdom.
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abstract = "We summarise some of our recent works on L∞-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of L∞-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of L∞-quasi-isomorphisms, and we propose a twistor space action.",
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note = "19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018; London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory ; Conference date: 12-08-2018 Through 18-08-2018",
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Jurčo, B, Macrelli, T, Raspollini, L, Saemann, C & Wolf, M 2019, 'L∞-Algebras, the BV Formalism, and Classical Fields' Paper presented at London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory, Durham, United Kingdom, 12/08/18 - 18/08/18, .

L∞-Algebras, the BV Formalism, and Classical Fields. / Jurčo, Branislav; Macrelli, Tommaso; Raspollini, Lorenzo; Saemann, Christian; Wolf, Martin.

2019. Paper presented at London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory, Durham, United Kingdom.

Research output: Contribution to conferencePaper

TY - CONF

T1 - L∞-Algebras, the BV Formalism, and Classical Fields

AU - Jurčo, Branislav

AU - Macrelli, Tommaso

AU - Raspollini, Lorenzo

AU - Saemann, Christian

AU - Wolf, Martin

N1 - 19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

PY - 2019/3/7

Y1 - 2019/3/7

N2 - We summarise some of our recent works on L∞-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of L∞-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of L∞-quasi-isomorphisms, and we propose a twistor space action.

AB - We summarise some of our recent works on L∞-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of L∞-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of L∞-quasi-isomorphisms, and we propose a twistor space action.

KW - hep-th

M3 - Paper

ER -

Jurčo B, Macrelli T, Raspollini L, Saemann C, Wolf M. L∞-Algebras, the BV Formalism, and Classical Fields. 2019. Paper presented at London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory, Durham, United Kingdom.