5-dimensional Chern-Simons gauge theory on an interval: Massive spin-2 theory from symmetry breaking via boundary conditions

Mahdi Torabian (Department of Physics, Sharif University of Technology, Azadi Ave, 1458889694, Tehran, Iran)

In this note, we revisit the 4-dimensional theory of massive gravity through compactification of an extra dimension and geometric symmetry breaking. We dimensionally reduce the 5-dimensional topological Chern-Simons gauge theory of (anti) de Sitter group on an interval. We apply non-trivial boundary conditions at the endpoints to break all of the gauge symmetries. We identify different components of the gauge connection as invertible vierbein and spin-connection to interpret it as a gravitational theory. The effective field theory in four dimensions includes the dRGT potential terms and has a tower of Kaluza-Klein states without massless graviton in the spectrum. The UV cut of the theory is the Planck scale of the 5-dimensional gravity l1. If ζ is the scale of symmetry breaking and L is the length of the interval, then the masses of the lightest graviton m and the level n (for n<Ll1) KK gravitons mKK(n) are determined as m=(ζL1)12mKK(n)=nL1. The 4-dimensional Planck mass is mPl(Ll3)12 and we find the hierarchy ζ<m<L1<l1<mPl.

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      "source": "Elsevier", 
      "title": "5-dimensional Chern-Simons gauge theory on an interval: Massive spin-2 theory from symmetry breaking via boundary conditions"
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  "abstracts": [
    {
      "source": "Elsevier", 
      "value": "In this note, we revisit the 4-dimensional theory of massive gravity through compactification of an extra dimension and geometric symmetry breaking. We dimensionally reduce the 5-dimensional topological Chern-Simons gauge theory of (anti) de Sitter group on an interval. We apply non-trivial boundary conditions at the endpoints to break all of the gauge symmetries. We identify different components of the gauge connection as invertible vierbein and spin-connection to interpret it as a gravitational theory. The effective field theory in four dimensions includes the dRGT potential terms and has a tower of Kaluza-Klein states without massless graviton in the spectrum. The UV cut of the theory is the Planck scale of the 5-dimensional gravity <math><msup><mrow><mi>l</mi></mrow><mrow><mo>\u2212</mo><mn>1</mn></mrow></msup></math>. If \u03b6 is the scale of symmetry breaking and L is the length of the interval, then the masses of the lightest graviton m and the level n (for <math><mi>n</mi><mo>&lt;</mo><mi>L</mi><msup><mrow><mi>l</mi></mrow><mrow><mo>\u2212</mo><mn>1</mn></mrow></msup></math>) KK gravitons <math><msubsup><mrow><mi>m</mi></mrow><mrow><mi>KK</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msubsup></math> are determined as <math><mi>m</mi><mo>=</mo><msup><mrow><mo>(</mo><mi>\u03b6</mi><msup><mrow><mi>L</mi></mrow><mrow><mo>\u2212</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>\u226a</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mi>KK</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msubsup><mo>=</mo><mi>n</mi><msup><mrow><mi>L</mi></mrow><mrow><mo>\u2212</mo><mn>1</mn></mrow></msup></math>. The 4-dimensional Planck mass is <math><msub><mrow><mi>m</mi></mrow><mrow><mi>Pl</mi></mrow></msub><mo>\u223c</mo><msup><mrow><mo>(</mo><mi>L</mi><msup><mrow><mi>l</mi></mrow><mrow><mo>\u2212</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math> and we find the hierarchy <math><mi>\u03b6</mi><mo>&lt;</mo><mi>m</mi><mo>&lt;</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>\u2212</mo><mn>1</mn></mrow></msup><mo>&lt;</mo><msup><mrow><mi>l</mi></mrow><mrow><mo>\u2212</mo><mn>1</mn></mrow></msup><mo>&lt;</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>Pl</mi></mrow></msub></math>."
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Published on:
28 October 2020
Publisher:
Elsevier
Published in:
Physics Letters B , Volume 810 C (2020)

Article ID: 135841
DOI:
https://doi.org/10.1016/j.physletb.2020.135841
Copyrights:
The Author
Licence:
CC-BY-3.0

Fulltext files: