A conformally invariant σ-model in 4 dimensions

Felsager, Bjørn; Leinaas, Jon Magne

doi:10.1016/0370-2693(80)90856-4

Cited by 14 publications

(18 citation statements)

References 3 publications

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“…, X µ 4k−1 NPB which suggests a new formulation of both classical and quantum mechanics for this kind of object [23]. To identify the kind of physical object described by W GYM ∞ we need to recall the conformally invariant, 4k-dimensional, σ-model action introduced in [24], [14]:…”

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confidence: 99%

p -branes from generalized Yang-Mills theory

Ansoldi

Castro

Spallucci

2001

Class. Quantum Grav.

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Abstract. We consider the reduced, quenched version of a generalized Yang-Mills action in 4k-dimensional spacetime. This is a new kind of matrix theory which is mapped through the Weyl-Wigner-Moyal correspondence into a field theory over a non-commutative phase space. We show that the "classical" limit of this field theory is encoded into the effective action of an open, (4k−1)-dimensional, bulk brane enclosed by a dynamical, Chern-Simons type, (4k − 2)-dimensional, boundary brane. The bulk action is a pure volume term, while the boundary action carries all the dynamical degrees of freedom.

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confidence: 99%

p -branes from generalized Yang-Mills theory

Ansoldi

Castro

Spallucci

2001

Class. Quantum Grav.

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“…The latter property holds and can be seen by inspection. The former property is a straightforward extension of the results in [1,3] for the compact case. Given the stereographic projections defined by eq-(11) : R 2n → H 2n one can find a set of independent 2n + 1 frame vectors, E p , representing the pullback of the orthogonal frame vectors of the 2n + 1-dim pseudo-Euclidean manifold onto the Euclidean signature AdS 2n space :…”

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confidence: 59%

“…The "stereographic" maps are a particular class of conformal maps. The action of the conformal group in R 2n will furnish the remaining conformal maps [1,3]. Hence, we see here once again the interrelation between self-duality and conformal invariance.…”

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confidence: 60%

“…In particular, Self Dual unit charge instanton solutions were found which correspond to conformal ( stereographic) maps from R 2n → S 2n . These models [1] were the higher-dimensional extension of the SO(5) σ models of Feisager and Leinaas in 4D [3]. When p + 1 = odd, the authors [2] also built Lagrangians for bosonic extendons ( branes) , however, conformal invariance was lost.…”

Section: Introductionmentioning

confidence: 99%

“…It was shown by [1,3] (for the compact case the orthogonality condition is naturally modified to yield the metric of the S 2n ) that the orthogonality conditions eqs-(25) are the necessary and suf f icient conditions to show that the particular field configurations n i (x) given by (11), after extending the four dimensional result to any D = 2n, satisfy the double self duality conditions eq-(10). The orthogonality relation implies that the angles among any two vectors is preserved after the mapping and also that all the vectors , after the mapping, are of equal length ( this is not to say that their length equals the same as before the mapping).…”

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confidence: 99%

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On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

Castro¹

2004

Int. J. Mod. Phys. A

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It is shown that the large N limit of SU (N ) YM in curved m-dim backgrounds can be subsumed by a higher m + n dimensional gravitational theory which can be identified to an m-dim generally invariant gauge theory of diffs N , where N is an n-dim internal space ( Cho, Sho, Park, Yoon ). Based on these findings, a very plausible geometrical interpretation of the AdS/CF T correspondence could be given. Conformally invariant sigma models in D = 2n dimensions with target non-compact SO(2n, 1) groups are reviewed. Despite the non-compact nature of the SO(2n, 1) , the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal "stereographic" mappings of R 2n into the Euclidean signature AdS 2n spaces. The relation between Self Dual branes and Chern-Simons branes , High Dimensional Knots , follows. A detailed discussion on W ∞ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in AdS 4 . This AdS 4 spacetime higher spin theory should have a one-to-one correspondence to noncritical W ∞ strings propagating on AdS 4 × S 7 .

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One-loop corrections in the O(5) Skyrme model

Kafiev¹

1984

Theor Math Phys

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A conformally invariant σ-model in 4 dimensions

Cited by 14 publications

References 3 publications

p -branes from generalized Yang-Mills theory

p -branes from generalized Yang-Mills theory

On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

One-loop corrections in the O(5) Skyrme model

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