Details
| Original language | English |
|---|---|
| Article number | 2350035 |
| Number of pages | 21 |
| Journal | Reviews in mathematical physics |
| Volume | 36 |
| Issue number | 1 |
| Early online date | 21 Oct 2023 |
| Publication status | Published - Feb 2024 |
Abstract
We consider Yang–Mills theory with a compact structure group G on a Lorentzian 4-manifold M = R×Σ such that gauge transformations become identity on a submanifold S of Σ (framing over S ⊂ Σ). The space S is not necessarily a boundary of Σ and can have dimension k ≤ 3. Framing of gauge bundles over S ⊂ Σ demands introduction of a G-valued function φS with support on S and modification of Yang–Mills equations along R × S ⊂ M. The fields φS parametrize non-equivalent flat connections mapped into each other by a dynamical group GS changing gauge frames over S. It is shown that the charged condensate φS is the Stueckelberg field generating an effective mass of gluons in the domain S of space Σ and keeping them massless outside S. We argue that the local Stueckelberg field φS can be responsible for color confinement. We also briefly discuss local breaking of symmetries in gravity. It is shown that framing of the tangent bundle over a subspace of spacetime makes gravitons massive in this subspace.
Keywords
- Gauge theories, symmetry breaking
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Reviews in mathematical physics, Vol. 36, No. 1, 2350035, 02.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Yang–Mills–Stueckelberg theories, framing and local breaking of symmetries
AU - Popov, Alexander D.
N1 - This work was supported by the Deutsche Forschungsgemeinschaft grant LE 838/19.
PY - 2024/2
Y1 - 2024/2
N2 - We consider Yang–Mills theory with a compact structure group G on a Lorentzian 4-manifold M = R×Σ such that gauge transformations become identity on a submanifold S of Σ (framing over S ⊂ Σ). The space S is not necessarily a boundary of Σ and can have dimension k ≤ 3. Framing of gauge bundles over S ⊂ Σ demands introduction of a G-valued function φS with support on S and modification of Yang–Mills equations along R × S ⊂ M. The fields φS parametrize non-equivalent flat connections mapped into each other by a dynamical group GS changing gauge frames over S. It is shown that the charged condensate φS is the Stueckelberg field generating an effective mass of gluons in the domain S of space Σ and keeping them massless outside S. We argue that the local Stueckelberg field φS can be responsible for color confinement. We also briefly discuss local breaking of symmetries in gravity. It is shown that framing of the tangent bundle over a subspace of spacetime makes gravitons massive in this subspace.
AB - We consider Yang–Mills theory with a compact structure group G on a Lorentzian 4-manifold M = R×Σ such that gauge transformations become identity on a submanifold S of Σ (framing over S ⊂ Σ). The space S is not necessarily a boundary of Σ and can have dimension k ≤ 3. Framing of gauge bundles over S ⊂ Σ demands introduction of a G-valued function φS with support on S and modification of Yang–Mills equations along R × S ⊂ M. The fields φS parametrize non-equivalent flat connections mapped into each other by a dynamical group GS changing gauge frames over S. It is shown that the charged condensate φS is the Stueckelberg field generating an effective mass of gluons in the domain S of space Σ and keeping them massless outside S. We argue that the local Stueckelberg field φS can be responsible for color confinement. We also briefly discuss local breaking of symmetries in gravity. It is shown that framing of the tangent bundle over a subspace of spacetime makes gravitons massive in this subspace.
KW - Gauge theories
KW - symmetry breaking
UR - http://www.scopus.com/inward/record.url?scp=85175460642&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2110.00405
DO - 10.48550/arXiv.2110.00405
M3 - Article
AN - SCOPUS:85175460642
VL - 36
JO - Reviews in mathematical physics
JF - Reviews in mathematical physics
SN - 0129-055X
IS - 1
M1 - 2350035
ER -