Tensor hierarchies and Leibniz algebras

Lavau, Sylvain

doi:10.1016/j.geomphys.2019.05.014

Cited by 32 publications

(49 citation statements)

References 24 publications

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“…It has recently been shown that any Leibniz algebra canonically (via a differential graded Lie algebra, or equivalently, an infinity-enhanced Leibniz algebra [58]) gives rise to an L ∞ algebra [59]. It would be interesting to compare the L ∞ algebra constructed in that way with the one presented here, not least since in the application to gauged supergravity, the relevant differential graded Lie algebra can be understood as coming from a tensor hierarchy algebra [60,61].…”

Section: Discussionmentioning

confidence: 96%

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

Cederwall

Palmkvist

2020

J. High Energ. Phys.

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The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns out to be a tensor hierarchy algebra rather than a Borcherds superalgebra. This tensor hierarchy algebra is a non-contragredient superalgebra, generically infinite-dimensional, which is a double extension of the structure algebra of the extended geometry. We use it to perform a (partial) analysis of the gauge structure in terms of an L ∞ algebra for extended geometries based on finite-dimensional structure groups. An invariant pseudo-action is also given in these cases. We comment on the continuation to infinite-dimensional structure groups. An accompanying paper [ ] deals with the mathematical construction of the tensor hierarchy algebras.

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Section: Discussionmentioning

confidence: 96%

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

Cederwall

Palmkvist

2020

J. High Energ. Phys.

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“…We can now derive some further consequences from the Leibniz relations, in particular from the closure relation (1.7), 4) and symmetrizing (2.3) in x, y we have…”

Section: Leibniz Algebrasmentioning

confidence: 99%

“…In this paper we construct the general gauge theory of Leibniz-Loday algebras [1][2][3][4][5][6], which are algebraic structures generalizing the notion of Lie algebras. These structures have appeared in the context of duality covariant formulations of gauged supergravity [7][8][9][10] and of string/M-theory [11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Leibniz Gauge Theories and Infinity Structures

Bonezzi

Hohm

2020

Commun. Math. Phys.

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We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based on 'tensor hierarchies', which describe towers of p-form gauge fields transforming under non-abelian gauge symmetries and which have been constructed up to low levels. Here we define 'infinity-enhanced Leibniz algebras' that guarantee the existence of consistent tensor hierarchies to arbitrary level. We contrast these algebras with strongly homotopy Lie algebras (L ∞ algebras), which can be used to define topological field theories for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries an associated L ∞ algebra, which we discuss.

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“…The recent resurgence of physics interest in L ∞ -algebras (e.g. [27][28][29][30][31][32][33][34][35][36][37][38]) mostly centres on gauge symmetries of classical theories. (Most relevant here is [28], which articulates the lore that classical BV master actions have canonical associated L ∞ -algebras [16,[39][40][41][42][43][44][45][46][47][48][49][50]).…”

Section: Jhep07(2019)115mentioning

confidence: 99%

The L∞-algebra of the S-matrix

Arvanitakis

2019

J. High Energ. Phys.

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We point out that the one-particle-irreducible vacuum correlation functions of a QFT are the structure constants of an L ∞-algebra, whose Jacobi identities hold whenever there are no local gauge anomalies. The LSZ prescription for S-matrix elements is identified as an instance of the "minimal model theorem" of L ∞-algebras. This generalises the algebraic structure of closed string field theory to arbitrary QFTs with a mass gap and leads to recursion relations for amplitudes (albeit ones only immediately useful at tree-level, where they reduce to Berends-Giele-style relations as shown in [1]).

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Tensor hierarchies and Leibniz algebras

Cited by 32 publications

References 24 publications

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

Leibniz Gauge Theories and Infinity Structures

The L∞-algebra of the S-matrix

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