Yang-Mills instantons and dyons on homogeneous G 2-manifolds

Bauer, Irina; Иванова, Т. А.; Lechtenfeld, Olaf; Lubbe, Felix

doi:10.1007/jhep10(2010)044

Cited by 33 publications

(67 citation statements)

References 60 publications

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“…Higher-dimensional instanton equations generalise the self-dual YangMills equations in four dimensions, and were first constructed in [62][63][64]. The instanton condition can be reformulated as a G 2 invariant constraint [36,37,[65][66][67][68][69][70][71][72][73], and explicit solutions to the instanton condition on certain G 2 manifolds are also known [74,75]. Here, we show that the G 2 instanton condition is implied by a supersymmetry constraint in string compactifications, and that it, in turn, implies the Yang-Mills equations as an equation of motion of the theory.…”

Section: Jhep11(2016)016mentioning

confidence: 99%

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

Ossa

Larfors

Svanes

2016

J. High Energ. Phys.

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Abstract:We describe the infinitesimal moduli space of pairs (Y, V ) where Y is a manifold with G 2 holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G 2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli H 1 d A (Y, End(V )) plus the moduli of the G 2 structure preserving the instanton condition. The latter piece is contained in H 1 d θ (Y, T Y ), and is given by the kernel of a mapF which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the mapF is given in terms of the curvature of the bundle and maps, and moreover can be used to define a cohomology on an extension bundle of T Y by End(V ). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on (Y, V ) when α = 0.

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Section: Jhep11(2016)016mentioning

confidence: 99%

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

Ossa

Larfors

Svanes

2016

J. High Energ. Phys.

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“…It is not difficult to show (see e.g. [14]) that the YangMills equations on I × S 3 after substituting (3.2) and (3.3) reduce to the ordinary matrix differential equations…”

Section: Jhep11(2017)017mentioning

confidence: 99%

“…Here, the non-stable S 4 transformations act by permuting the coordinate axes, but two equivalent choices give the same equations. In the S 3 case, we choose the direction (1, 1, 1) and put 14) where ψ(t) is some other real-valued function of t ∈ (− π 2 , π 2 ). This ansatz leads to the simplifications…”

Section: Jhep11(2017)017mentioning

confidence: 99%

“…By continuity, shorter periods cannot be attained, but there should exist a 2π-periodic solution for a special value of k. Since dn[u; k] has a period of 2K(k), where K(k) is the complete elliptic integral of the first kind (see e.g. the appendix of [14] for a brief discussion of Jacobi functions), the periodicity condition is satisfied if [18,19] …”

Section: Jhep11(2017)017mentioning

confidence: 99%

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Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

Иванова¹,

Lechtenfeld

Popov

2017

J. High Energ. Phys.

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We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS 4 and anti-de Sitter AdS 4 spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in R 3 under the influence of a quartic potential. Then we describe magnetic and electric-magnetic solutions, both Abelian and non-Abelian, all having finite energy and finite action. A similar reduction on anti-de Sitter space also yields Yang-Mills solutions with finite energy and action. We propose a lower bound for the action on both backgrounds. Employing another metric on AdS 4 , the SU(2) Yang-Mills equations are reduced to an analytic continuation of the above particle mechanics from R 3 to R 2,1 . We discuss analytical solutions to these equations, which produce infinite-action configurations. After a Euclidean continuation of dS 4 and AdS 4 we also present self-dual (instanton-type) Yang-Mills solutions on these backgrounds.

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“…Refs. [16][17][18] where _ X a ≔ dX a =dt and e 0 ≔ dt. It is not difficult to show (see, e.g., Ref.…”

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confidence: 99%

Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

Иванова¹,

Lechtenfeld

Popov

2017

Phys. Rev. Lett.

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We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS 4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS 4 as R × S 3 , via an SU(2)-equivariant ansatz, we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τ ∈ R is given byB a ¼ − 1 2 I a =ðR 2 cosh 2 τÞ, where I a for a ¼ 1, 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value − 1 2 jðj þ 1Þð2j þ 1Þπ 3 in a spin-j representation.Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.

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Yang-Mills instantons and dyons on homogeneous G 2-manifolds

Cited by 33 publications

References 60 publications

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

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