Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly
Abstract Actions for noncommutative (NC) gauge field theories can be expanded perturbatively in powers of the noncommutativity parameter $$\theta $$ θ using the Seiberg–Witten map between ordinary classical fields and their NC counterparts. The leading order term represents classical ( $$\theta =0$$...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-08-01
|
| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-10657-7 |
| _version_ | 1828293718842540032 |
|---|---|
| author | Dušan Ɖorđević Dragoljub Gočanin |
| author_facet | Dušan Ɖorđević Dragoljub Gočanin |
| author_sort | Dušan Ɖorđević |
| collection | DOAJ |
| description | Abstract Actions for noncommutative (NC) gauge field theories can be expanded perturbatively in powers of the noncommutativity parameter $$\theta $$ θ using the Seiberg–Witten map between ordinary classical fields and their NC counterparts. The leading order term represents classical ( $$\theta =0$$ θ = 0 ) action while higher-order terms give us $$\theta $$ θ -dependent NC corrections that ought to capture some aspects of quantum gravity. Building on previous work of Aschieri and Castellani on NC Chern–Simons (CS) gauge and gravity theories, showing that non-trivial $$\theta $$ θ -dependence exists only for spacetime dimensions $$D\ge 5$$ D ≥ 5 , we investigate a correlated effect of these extra spatial dimensions and noncommutativity on four-dimensional physics, up to first-order in $$\theta $$ θ . Assuming that one spatial dimension is compactified into a circle, we apply the Kaluza–Klein reduction procedure on the NC $$D=5$$ D = 5 CS theory for the conformal gauge group SO(4, 2), to obtain an effective, $$\theta $$ θ -dependent four-dimensional theory of gravity that has Einstein–Hilbert gravity with negative cosmological constant as its commutative limit. We derive field equations for this modified theory of gravity and study the effect of NC interactions on some classical geometries, such as the AdS-Schwarzschild black hole. We find that this NC background spacetime gives rise to chiral gravitational anomaly due to the nonvanishing $$\theta $$ θ -dependent Pontryagin density. |
| first_indexed | 2024-04-13T11:24:50Z |
| format | Article |
| id | doaj.art-edd9438e58ad480d997db4c7fdd979f2 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-13T11:24:50Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-edd9438e58ad480d997db4c7fdd979f22022-12-22T02:48:43ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522022-08-0182811510.1140/epjc/s10052-022-10657-7Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomalyDušan Ɖorđević0Dragoljub Gočanin1Faculty of Physics, University of BelgradeFaculty of Physics, University of BelgradeAbstract Actions for noncommutative (NC) gauge field theories can be expanded perturbatively in powers of the noncommutativity parameter $$\theta $$ θ using the Seiberg–Witten map between ordinary classical fields and their NC counterparts. The leading order term represents classical ( $$\theta =0$$ θ = 0 ) action while higher-order terms give us $$\theta $$ θ -dependent NC corrections that ought to capture some aspects of quantum gravity. Building on previous work of Aschieri and Castellani on NC Chern–Simons (CS) gauge and gravity theories, showing that non-trivial $$\theta $$ θ -dependence exists only for spacetime dimensions $$D\ge 5$$ D ≥ 5 , we investigate a correlated effect of these extra spatial dimensions and noncommutativity on four-dimensional physics, up to first-order in $$\theta $$ θ . Assuming that one spatial dimension is compactified into a circle, we apply the Kaluza–Klein reduction procedure on the NC $$D=5$$ D = 5 CS theory for the conformal gauge group SO(4, 2), to obtain an effective, $$\theta $$ θ -dependent four-dimensional theory of gravity that has Einstein–Hilbert gravity with negative cosmological constant as its commutative limit. We derive field equations for this modified theory of gravity and study the effect of NC interactions on some classical geometries, such as the AdS-Schwarzschild black hole. We find that this NC background spacetime gives rise to chiral gravitational anomaly due to the nonvanishing $$\theta $$ θ -dependent Pontryagin density.https://doi.org/10.1140/epjc/s10052-022-10657-7 |
| spellingShingle | Dušan Ɖorđević Dragoljub Gočanin Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly European Physical Journal C: Particles and Fields |
| title | Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly |
| title_full | Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly |
| title_fullStr | Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly |
| title_full_unstemmed | Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly |
| title_short | Noncommutative $$D=5$$ D = 5 Chern–Simons gravity: Kaluza–Klein reduction and chiral gravitational anomaly |
| title_sort | noncommutative d 5 d 5 chern simons gravity kaluza klein reduction and chiral gravitational anomaly |
| url | https://doi.org/10.1140/epjc/s10052-022-10657-7 |
| work_keys_str_mv | AT dusanɖorđevic noncommutatived5d5chernsimonsgravitykaluzakleinreductionandchiralgravitationalanomaly AT dragoljubgocanin noncommutatived5d5chernsimonsgravitykaluzakleinreductionandchiralgravitationalanomaly |