A cohomological obstruction in higher-dimensional Chern–Simons gauge theories

Palese, Marcella; Winterroth, Ekkehart

doi:10.1142/S0219887822500323

A cohomological obstruction in higher-dimensional Chern–Simons gauge theories

Nov 17, 2021

20 pages

Published in:

Int.J.Geom.Meth.Mod.Phys. 19 (2022) 03, 2250032,
Physics 19 (2022) 2250032

Published: Dec 15, 2021

e-Print:

2111.09247 [hep-th]

DOI:

10.1142/S0219887822500323

View in:

pdf

reference search0 citations

Citations per year

0 Citations

Abstract: (WSP)

We study a set of cohomology classes which emerge in the cohomological formulations of the calculus of variations as obstructions to the existence of (global) solutions of the Euler–Lagrange equations of Chern–Simons gauge theories in higher dimensions 2p + 1 > 3.

Note:

20 pages. arXiv admin note: text overlap with arXiv:2103.03037

Cohomological formulation of the calculus of variations
cohomological formulation of the calculus of variations
Chern–Weil theory
Chern–Simons theories
Chern–Simons gravity
cohomology
gauge field theory
higher-dimensional
Chern-Simons term
field equations: solution

References(32)

Figures(0)

[1]

Symmetry transformations of extremals and higher conserved quantities: Invariant Yang–Mills connections

Luca Accornero
(
- Utrecht U.
)
,
Marcella Palese
(
- Turin U.
)

- J.Math.Phys. 62 (2021) 4, 043504
•
e-Print:
- 1910.11688
•
DOI:
- 10.1063/5.0038533

[2]

On the existence of global variational principles

I.M. Anderson
,
T. Duchamp

- Am.J.Math. 102 (1980) 781-868
•
DOI:
- 10.2307/2374195

[3]

Introduction to the variational bicomplex, in Mathematical Aspects of Classical Field Theory, Contemporary Mathematics, Vol. 132, M. J. Gotayet (eds.)

I.M. Anderson

•
DOI:
- 10.1090/conm

[4]

Exact solutions in higher-dimensional Lovelock and AdS $_{5}$ Chern-Simons gravity

Francesco Bajardi
(
- Naples U. and
- INFN, Naples
)
,
Daniele Vernieri
(
- Naples U. and
- INFN, Naples
)
,
Salvatore Capozziello
(
- Naples U. and
- INFN, Naples and
- SSM, Naples and
- TUSUR, Tomsk
)

- JCAP 11 (2021) 11, 057,
- JCAP 11 (2021) 11, 057
•
e-Print:
- 2106.07396
•
DOI:
- 10.1088/1475-7516/2021/11/057

[5]

Über die Erhaltungssätze der Elektrodynamik

E. Bessel-Hagen

- Math.Ann. 84 (1921) 258-276
•
DOI:
- 10.1007/BF01459410

[6]

A Covariant formalism for Chern-Simons gravity

Andrzej Borowiec
(
- Wroclaw U.
)
,
Marco Ferraris
(
- Turin U., Math Dept.
)
,
Mauro Francaviglia
(
- Turin U., Math Dept.
)

- J.Phys.A 36 (2003) 2589-2598
•
e-Print:
- hep-th/0301146
•
DOI:
- 10.1088/0305-4470/36/10/318

[7]

The geometry of the bundle of connections

M. Castrillon Lopez
,
J. Munoz Masque

- Math.Z. 236 (2001) 797-811
•
DOI:
- 10.1007/PL00004852

[8]

Variational derivatives in locally Lagrangian field theories and Noether–Bessel-Hagen currents

- Int.J.Geom.Meth.Mod.Phys. 13 (2016) 08, 1650067
•
e-Print:
- 1601.07193
•
DOI:
- 10.1142/S0219887816500675

[9]

Topological Gauge Theory of Gravity in Five-dimensions and All Odd Dimensions

Ali H. Chamseddine
(
- Zurich U.
)

- Phys.Lett.B 233 (1989) 291-294
•
DOI:
- 10.1016/0370-2693(89)91312-9

[10]

Topological gravity and supergravity in various dimensions

Ali H. Chamseddine
(
- Zurich U.
)

- Nucl.Phys.B 346 (1990) 213-234
•
DOI:
- 10.1016/0550-3213(90)90245-9

[11]

Some cohomology classes in principal fiber bundles and their application to Riemannian geometry

S.S. Chern
,
J. Simons

- Proc.Nat.Acad.Sci. 68 (1971) 791-794
•
DOI:
- 10.1073/pnas.68.4.791

[12]

Characteristic forms and geometric invariants

Shiin-Shen Chern
(
- UC, Berkeley
)
,
James Simons
(
- SUNY, Stony Brook
)

- Annals Math. 99 (1974) 48-69
•
DOI:
- 10.2307/1971013

[13]

Topologically Massive Gauge Theories

- Annals Phys. 140 (1982) 372-411,
- Annals Phys. 185 (1988) 406 (erratum),
- Annals Phys. 281 (2000) 409-449
•
DOI:
- 10.1016/0003-4916(82)90164-6

[14]

Local variational problems and conservation laws

M. Ferraris
,
M. Palese
,
E. Winterroth

- Differ.Geom.Appl. 29 (2011) S80-S85
•
DOI:
- 10.1016/j.difgeo.2011.04.011

[15]

Variationally equivalent problems and variations of Noether currents

M. Francaviglia
,
M. Palese
,
E. Winterroth

- Int.J.Geom.Meth.Mod.Phys. 10 (2013) 1220024

[16]

Noether conservation laws in higher dimensional Chern-Simons theory

Giovanni Giachetta
(
- Camerino U.
)
,
Luigi Mangiarotti
(
- Camerino U.
)
,
Gennadi Sardanashvily
(
- Moscow State U.
)

- Mod.Phys.Lett.A 18 (2003) 2645-2651
•
e-Print:
- math-ph/0310067
•
DOI:
- 10.1142/S0217732303012313

[17]

Fibre Bundles, 3rd edn., Graduate Texts in Mathematics, Vol. 20

D. Husemoller

•
DOI:
- 10.1007/978-1-4757-2261-1

[18]

Foundations of Differential Geometry, Vol. I

S. Kobayashi
,
K. Nomizu

[18]

Vol. II (John

[19]

Variational sequences on finite order jet spaces, in Differential Geometry and its Applications, Proc. Conf., J. JanyškaD (eds.)

D. Krupka

[20]

Characteristic Classes, Annals of Mathematics Studies, Vol. 76 (Princeton University Press, Princeton, NJ,)

J.W. Milnor
,
J.D. Stasheff

•
DOI:
- 10.1515/9781400881826

[21]

Invariante Variations probleme, Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. II235-257

E. Noether

[22]

Variational sequences, representation sequences and applications in physics

M. Palese
,
O. Rossi
,
E. Winterroth
,
J. Musilov

- SIGMA 12 (2016) 045

[23]

Topological obstructions in Lagrangian field theories, with an application to 3D Chern–Simons gauge theory

- J.Math.Phys. 58 (2017) 2, 023502
•
e-Print:
- 1608.05789
•
DOI:
- 10.1063/1.4975336

[24]

The Geometry of Jet Bundles, London Mathematical Society Lecture Note Series, Vol. 142 (Cambridge University Press, Cambridge, UK,)

D.J. Saunders

•
DOI:
- 10.1017/CBO9780511526411

1-25 of 32
1
2
25 / page