A note on SU(∞) classical Yang-Mills theories

Floratos, E.G.; Iliopoulos, J.; Tiktopoulos, George

doi:10.1016/0370-2693(89)90867-8

Cited by 100 publications

(116 citation statements)

References 7 publications

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“…The final result is obtained by summing the remaining four terms (13,24), (24,13), (14,23) and (23,14), which after using momentum conservation and the on-shell condition, gives…”

Section: Tree Level Amplitudesmentioning

confidence: 99%

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Large N WZW field theory of N=2 strings

1998

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We explore the quantum properties of self-dual gravity formulated as a large N two-dimensional WZW sigma model. Using a non-trivial classical background, we show that a (2, 2) space-time is generated. The theory contains an infinite series of higher point vertices. At tree level we show that, in spite of the presence of higher than cubic vertices, the on-shell 4 and higher point functions vanish, indicating that this model is related with the field theory of closed N = 2 strings. We examine the one-loop on-shell 3-point amplitude and show that it is ultra-violet finite.

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“…The final result is obtained by summing the remaining four terms (13,24), (24,13), (14,23) and (23,14), which after using momentum conservation and the on-shell condition, gives…”

Section: Tree Level Amplitudesmentioning

confidence: 99%

“…But, as a consequence of the highly constrained kinematics in (2, 2) signature, the term in brackets in (14) vanishes when all momenta are on-shell [4,17]. Therefore, the total on-shell tree level 4-point amplitude for (1) vanishes.…”

Section: Tree Level Amplitudesmentioning

confidence: 99%

Large N WZW field theory of N=2 strings

1998

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“…[6] The SU(∞) Yang-Mills theory [5] has been put forward in the context of the study of membrane theory. [6] To make our discussion self-contained, we review the SU(∞) Yang-Mills theory [5] in this section.…”

Section: Review Of Su(∞) Yang-mills Theorymentioning

confidence: 99%

“…Recently Floratos et al [5] offered a model with the gauge symmetry of an infinite dimensional group. The symmetry, SU(∞) is being eagerly investigated in the study of membrane theory.…”

Section: Introductionmentioning

confidence: 99%

U(∞) GAUGE THEORY FROM HIGHER DIMENSIONS

Shiraishi

1992

Int. J. Mod. Phys. A

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We show that classical U(∞) gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the infinite-dimensional symmetry can be taken as spontaneously broken. Monopole solutions are examined in the model for scalar and gauge fields. An extension to gravity is also discussed.

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“…The algebras are also related to S U (Go) Yang-Mills theories and membranes [13][14][15] and are possible candidates * Permanent address: Institute for Theoretical and Experimental Physics, 117258 Moscow, Russia ** Bitnet: SJT@DMUMPIWH for the universal algebra in the description of all integrable interactions which arise in string theory [16].…”

Section: Introductionmentioning

confidence: 99%

Dynamical systems on quantum tori Lie algebras

1993

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Abstract.We use quantum tori Lie algebras (QTLA), which are a one-parameter family of sub-algebras of gl~, to describe local and non-local versions of the Toda systems. It turns out that the central charge of QTLA is responsible for the non-locality. There are two regimes in the local systems -conformal for irrational values of the parameter and non-conformal and integrable for its rational values. We also consider infinite-dimensional analogs of rigid tops. Some of these systems give rise to "quantized" (magneto-)hydrodynamic equations of an ideal fluid on a torus. We also consider infinite dimensional versions of the integrable Euler and Clebsch cases.

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A note on SU(∞) classical Yang-Mills theories

Cited by 100 publications

References 7 publications

Large N WZW field theory of N=2 strings

Large N WZW field theory of N=2 strings

U(∞) GAUGE THEORY FROM HIGHER DIMENSIONS

Dynamical systems on quantum tori Lie algebras

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