Built on

V. G. Kupriyanov, “Noncommutative deformation of Chern–Simons theory,” Eur. Phys. J. C 80
Original
1905
Earlier work this paper cites.
K. İ. Berktav, “Stacky formulations of Einstein gravity,” arXiv:1907.00665 [math.AG]
Original
1907
Earlier work this paper cites.
B. Jurčo, L. Raspollini, C. Sämann and M. Wolf, “Loop Amplitudes and Quantum Homotopy algebras,” JHEP 07
Original
1912
Earlier work this paper cites.
R. Jackiw, “Invariance, Symmetry and Periodicity in Gauge Theories,” Acta Phys. Austr. Suppl. XXII
1980
Earlier work this paper cites.
I. A. Batalin and G. A. Vilkovisky, “Gauge algebra and quantization,” Phys. Lett. B 102
1981
Earlier work this paper cites.
R. D’Auria and T. Regge, “Gravity theories with asymptotically flat instantons,” Nucl. Phys. B 195
1982
Earlier work this paper cites.
A. A. Tseytlin, “On The First Order Formalism In Quantum Gravity,” J. Phys. A 15
1982
Earlier work this paper cites.
F. A. Berends, G. J. H. Burgers and H. van Dam, “On the theoretical problems in constructing interactions involving higher spin massless particles,” Nucl. Phys. B 260
1985
Earlier work this paper cites.
L. Baulieu and M. P. Bellon, “ p p -forms and supergravity: Gauge symmetries in curved space,” Nucl. Phys. B 266
1986
Earlier work this paper cites.
E. Witten, “ ( 2 + 1 ) (2+1) -dimensional gravity as an exactly soluble system,” Nucl. Phys. B 311
1988
Earlier work this paper cites.
M. Henneaux, “Lectures on the antifield-BRST formalism for gauge theories,” Nucl. Phys. Proc. Suppl. A 18
1990
Earlier work this paper cites.
S. B. Giddings, “Spontaneous breakdown of diffeomorphism invariance,” Phys. Lett. B 268
1991
Earlier work this paper cites.
D. Birmingham, M. Blau, M. Rakowski and G. Thompson, “Topological field theory,” Phys. Rept. 209
1991
Earlier work this paper cites.
B. Zwiebach, “Closed string field theory: Quantum action and the BV master equation,” Nucl. Phys. B 390
1993
Earlier work this paper cites.
T. Lada and J. Stasheff, “Introduction to sh Lie algebras for physicists,” Int. J. Theor. Phys. 32
1993
Earlier work this paper cites.
O. Moritsch, M. Schweda and S. P. Sorella, “Algebraic structure of gravity with torsion,” Class. Quant. Grav. 11
1994
Earlier work this paper cites.
T. Lada and M. Markl, “Strongly homotopy Lie algebras,” Commun. Algebra 23
1995
Earlier work this paper cites.
J. Stasheff, “The (secret?) homological algebra of the Batalin-Vilkovisky approach,” Contemp. Math. 219
1998
Earlier work this paper cites.

Similar

S. Carlip, Quantum Gravity in 2+1 Dimensions (Cambridge University Press, 1998)
1998
Cited alongside, same era.
O. Piguet, “Ghost equations and diffeomorphism invariant theories,” Class. Quant. Grav. 17
2000
Cited alongside, same era.
M. Montesinos, R. Romero and D. Gonzalez, “The gauge symmetries of f ⁡ ( R ) f(R) gravity with torsion in the Cartan formalism,” Class. Quant. Grav. 37
Original
2001
Cited alongside, same era.
H. Kajiura, “Homotopy algebra morphism and geometry of classical string field theory,” Nucl. Phys. B 630
2002
Cited alongside, same era.
M. Kontsevich, “Deformation quantization of Poisson manifolds,” Lett. Math. Phys. 66
2003
Cited alongside, same era.

Then

N. Dragon and F. Brandt, “BRST symmetry and cohomology,” in: Strings, Gauge Fields, and the Geometry Behind
Original
2012
Later among the works it cites.
R. Blumenhagen, M. Fuchs, F. Hassler, D. Lüst and R. Sun, “Nonassociative deformations of geometry in double field theory,” JHEP 1404
Original
2014
Later among the works it cites.
D. Mylonas, P. Schupp and R. J. Szabo, “Non-geometric fluxes, quasi-Hopf twist deformations and nonassociative quantum mechanics,” J. Math. Phys. 55
Original
2014
Later among the works it cites.
P. Aschieri and R. J. Szabo, “Triproducts, nonassociative star products and geometry of R R -flux string compactifications,” J. Phys. Conf. Ser. 634
Original
2015
Later among the works it cites.
R. Blumenhagen and M. Fuchs, “Towards a theory of nonassociative gravity,” JHEP 1607

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2020

$L_{\infty}$-Algebras of Einstein-Cartan-Palatini Gravity

Ćirić, Marija Dimitrijević, Giotopoulos, Grigorios, Radovanović, Voja et al.

Understand

We give a detailed account of the cyclic $L_\infty$-algebra formulation of general relativity with cosmological constant in the Einstein-Cartan-Palatini formalism on spacetimes of arbitrary dimension and signature, which encompasses all symmetries, field equations and Noether identities of gravity without matter fields.

We present a local formulation as well as a global covariant framework, and an explicit isomorphism between the two $L_\infty$-algebras in the case of parallelizable spacetimes.
By duality, we show that our $L_\infty$-algebras describe the complete BV-BRST formulation of Einstein-Cartan-Palatini gravity.
We give a general description of how to extend on-shell redundant symmetries in topological gauge theories to off-shell correspondences between symmetries in terms of quasi-isomorphisms of $L_\infty$-algebras.

Built on

V. G. Kupriyanov, “Noncommutative deformation of Chern–Simons theory,” Eur. Phys. J. C 80
Original
1905
Earlier work this paper cites.
K. İ. Berktav, “Stacky formulations of Einstein gravity,” arXiv:1907.00665 [math.AG]
Original
1907
Earlier work this paper cites.
B. Jurčo, L. Raspollini, C. Sämann and M. Wolf, “Loop Amplitudes and Quantum Homotopy algebras,” JHEP 07
Original
1912
Earlier work this paper cites.
R. Jackiw, “Invariance, Symmetry and Periodicity in Gauge Theories,” Acta Phys. Austr. Suppl. XXII
1980
Earlier work this paper cites.
I. A. Batalin and G. A. Vilkovisky, “Gauge algebra and quantization,” Phys. Lett. B 102
1981
Earlier work this paper cites.
R. D’Auria and T. Regge, “Gravity theories with asymptotically flat instantons,” Nucl. Phys. B 195
1982
Earlier work this paper cites.
A. A. Tseytlin, “On The First Order Formalism In Quantum Gravity,” J. Phys. A 15
1982
Earlier work this paper cites.
F. A. Berends, G. J. H. Burgers and H. van Dam, “On the theoretical problems in constructing interactions involving higher spin massless particles,” Nucl. Phys. B 260
1985
Earlier work this paper cites.
L. Baulieu and M. P. Bellon, “ p p -forms and supergravity: Gauge symmetries in curved space,” Nucl. Phys. B 266
1986
Earlier work this paper cites.
E. Witten, “ ( 2 + 1 ) (2+1) -dimensional gravity as an exactly soluble system,” Nucl. Phys. B 311
1988
Earlier work this paper cites.
M. Henneaux, “Lectures on the antifield-BRST formalism for gauge theories,” Nucl. Phys. Proc. Suppl. A 18
1990
Earlier work this paper cites.
S. B. Giddings, “Spontaneous breakdown of diffeomorphism invariance,” Phys. Lett. B 268
1991
Earlier work this paper cites.
D. Birmingham, M. Blau, M. Rakowski and G. Thompson, “Topological field theory,” Phys. Rept. 209
1991
Earlier work this paper cites.
B. Zwiebach, “Closed string field theory: Quantum action and the BV master equation,” Nucl. Phys. B 390
1993
Earlier work this paper cites.
T. Lada and J. Stasheff, “Introduction to sh Lie algebras for physicists,” Int. J. Theor. Phys. 32
1993
Earlier work this paper cites.
O. Moritsch, M. Schweda and S. P. Sorella, “Algebraic structure of gravity with torsion,” Class. Quant. Grav. 11
1994
Earlier work this paper cites.
T. Lada and M. Markl, “Strongly homotopy Lie algebras,” Commun. Algebra 23
1995
Earlier work this paper cites.
J. Stasheff, “The (secret?) homological algebra of the Batalin-Vilkovisky approach,” Contemp. Math. 219
1998
Earlier work this paper cites.

Similar

S. Carlip, Quantum Gravity in 2+1 Dimensions (Cambridge University Press, 1998)
1998
Cited alongside, same era.
O. Piguet, “Ghost equations and diffeomorphism invariant theories,” Class. Quant. Grav. 17
2000
Cited alongside, same era.
M. Montesinos, R. Romero and D. Gonzalez, “The gauge symmetries of f ⁡ ( R ) f(R) gravity with torsion in the Cartan formalism,” Class. Quant. Grav. 37
Original
2001
Cited alongside, same era.
H. Kajiura, “Homotopy algebra morphism and geometry of classical string field theory,” Nucl. Phys. B 630
2002
Cited alongside, same era.
M. Kontsevich, “Deformation quantization of Poisson manifolds,” Lett. Math. Phys. 66
2003
Cited alongside, same era.

Then

N. Dragon and F. Brandt, “BRST symmetry and cohomology,” in: Strings, Gauge Fields, and the Geometry Behind
Original
2012
Later among the works it cites.
R. Blumenhagen, M. Fuchs, F. Hassler, D. Lüst and R. Sun, “Nonassociative deformations of geometry in double field theory,” JHEP 1404
Original
2014
Later among the works it cites.
D. Mylonas, P. Schupp and R. J. Szabo, “Non-geometric fluxes, quasi-Hopf twist deformations and nonassociative quantum mechanics,” J. Math. Phys. 55
Original
2014
Later among the works it cites.
P. Aschieri and R. J. Szabo, “Triproducts, nonassociative star products and geometry of R R -flux string compactifications,” J. Phys. Conf. Ser. 634
Original
2015
Later among the works it cites.
R. Blumenhagen and M. Fuchs, “Towards a theory of nonassociative gravity,” JHEP 1607

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

K. Fukaya, “Deformation theory, homological algebra and mirror symmetry,” in: Geometry and Physics of Branes

2003

Cited alongside, same era.

F. Girelli and H. Pfeiffer, “Higher gauge theory: Differential versus integral formulation,” J. Math. Phys. 45

2004

Cited alongside, same era.

M. Dimitrijević Ćirić, G. Giotopoulos, V. Radovanović and R. J. Szabo, “Homotopy Lie Algebras of Gravity and their Braided Deformations,” PoS CORFU 2019