Aspects of boundary conditions for non-Abelian gauge theories

Balachandran, A. P.; Nair, V. P.; Vaidya, Sachindeo

doi:10.1103/physrevd.100.045001

Cited by 3 publications

(4 citation statements)

References 49 publications

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“…All these structures also exist for the case of non-Abelian gauge theories such as QCD, with subtle consequences which are still not fully understood [3]. Unlike the case of the gauge group G(U(1)) of QED, the gauge group G(SU(3)) of, say, QCD, is non-Abelian.…”

Section: Introductionmentioning

confidence: 99%

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Superselection, Boundary Algebras and Duality in Gauge Theories

Balachandran,

Nair,

Pinzul

et al. 2021

Preprint

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We consider the generators of gauge transformations with test functions which do not vanish on the boundary of a spacelike region of interest. These are known to generate the edge degrees of freedom in a gauge theory. In this paper, we augment these by introducing the dual or magnetic analogue of such operators. We then study the algebra of these operators, focusing on implications for the superselection sectors of the gauge theory. A manifestly duality-invariant action is also considered, from which alternate descriptions which are SL(2, Z) transforms of each other can be obtained. We also comment on a number of issues related to local charges, definition of confinement and the appearance of interesting mathematical structures such as the Drinfel'd double and the Manin triple.

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Section: Introductionmentioning

confidence: 99%

“…So they cannot be implemented in an irreducible representation of A, a feature similar to the spontaneous breaking of the Lorentz transformations in the charged sectors of QED. Notice that what is 'broken' is the global group, such as SU (3).…”

Section: Introductionmentioning

confidence: 99%

Superselection, Boundary Algebras and Duality in Gauge Theories

Balachandran,

Nair,

Pinzul

et al. 2021

Preprint

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“…This is directly related to the choices of boundary conditions (see e.g. [10]). In our case, the framing over the boundary introduces non-dynamical degrees of freedom, and naïve imposition of constraints such as the Gauss law (4.20) leads to the loss of these data.…”

Section: Discussionmentioning

confidence: 99%

“…There is presently a revived and growing interest in the general allowed boundary conditions for gauge fields at infinity, either spatial or null (see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] for reviews, recent developments and references). The question of boundary conditions is directly related to the questions of allowed solutions, additional degrees of freedom, non-gauge symmetries of Yang-Mills theory etc.…”

Section: Introductionmentioning

confidence: 99%

A low-energy limit of Yang-Mills theory on de Sitter space

Cork

Kutluk

Lechtenfeld

et al. 2021

J. High Energ. Phys.

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We consider Yang-Mills theory with a compact structure group G on four-dimensional de Sitter space dS4. Using conformal invariance, we transform the theory from dS4 to the finite cylinder $$ \mathcal{I} $$ I × S3, where $$ \mathcal{I} $$ I = (−π/2, π/2) and S3 is the round three-sphere. By considering only bundles P → $$ \mathcal{I} $$ I × S3 which are framed over the temporal boundary ∂$$ \mathcal{I} $$ I × S3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂$$ \mathcal{I} $$ I × S3. We study the consequences of the framing on the variation of the action, and on the Yang-Mills equations. This allows for an infinite-dimensional moduli space of Yang-Mills vacua on dS4. We show that, in the low-energy limit, when momentum along $$ \mathcal{I} $$ I is much smaller than along S3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space $$ \mathcal{M} $$ M vac of gauge-inequivalent Yang-Mills vacua on S3. Since $$ \mathcal{M} $$ M vac ≅ C∞(S3, G)/G is a group manifold, the dynamics is expected to be integrable.

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Superselection, boundary algebras, and duality in gauge theories

et al. 2022

Self Cite

View full text Add to dashboard Cite

We consider the generators of gauge transformations with test functions which do not vanish on the boundary of a spacelike region of interest. These are known to generate the edge degrees of freedom in a gauge theory. In this paper, we augment these by introducing the dual or magnetic analog of such operators. We then study the algebra of these operators, focusing on implications for the superselection sectors of the gauge theory. A manifestly duality-invariant action is also considered, from which alternate descriptions which are SLð2; ZÞ transforms of each other can be obtained. We also comment on a number of issues related to local charges, definition of confinement and the appearance of interesting mathematical structures such as the Drinfel'd double and the Manin triple.

show abstract

Aspects of boundary conditions for non-Abelian gauge theories

Cited by 3 publications

References 49 publications

Superselection, Boundary Algebras and Duality in Gauge Theories

Superselection, Boundary Algebras and Duality in Gauge Theories

A low-energy limit of Yang-Mills theory on de Sitter space

Superselection, boundary algebras, and duality in gauge theories

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