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 -