A noncommutative deformation of topological field theory

García‐Compeán, Hugo; Paniagua, Pablo

doi:10.1007/s10714-005-0058-3

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…It is tempting to conjecture that, at least in the strong-coupling regime, these deformed moduli spaces, and the noncommutative open string theory, could be described by some sort of noncommutative topological sigma-model. Noncommutative versions of the standard topological field theories may be constructed by deforming the BRST algebras of observables [76]- [78].…”

Section: Open String Interpretationmentioning

confidence: 99%

Instantons, fluxons, and open gauge string theory

Seminara¹,

Szabo²

2005

Advances in Theoretical and Mathematical Physics

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Abstract:We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of noncommutative torus instantons is shown to map in a very precise way, at both the classical and quantum level, onto fluxon solutions on the noncommutative plane. The weak-coupling singularities of the usual Gross-Taylor string partition function for QCD on the torus are studied in the instanton representation and its double scaling limit, appropriate for the mapping onto noncommutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holomorphic differentials. The noncommutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.

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Section: Open String Interpretationmentioning

confidence: 99%

Instantons, fluxons, and open gauge string theory

Seminara¹,

Szabo²

2005

Advances in Theoretical and Mathematical Physics

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“…Recall that the structure constants totally antisymmetric f klm and the totally symmetric d klm of the gauge group G = U (N ) are given by the next relations [38,39] […”

Section: Simonsmentioning

confidence: 99%

One-loop Renormalized Coefficient of Noncommutative Supersymmetric Yang-Mills-Chern-Simons Gauge Theories in Three Dimensions

Estrada-Jiménez¹,

García‐Compeán²

2011

Preprint

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Recent studies of the AdS 4 /CF T 3 correspondence involve the construction of a peculiar supersymmetric gauge theory on the worldvolume of multiple M2s branes as a boundary field theory. Under suitable conditions the quantum theory becomes a noncommutative supersymmetric YM-CS gauge theory which call for an study of its renormalized perturbative corrections. As a preliminary step to more general consideration, the modification of the N = 3, 2, 1 supersymmetric YM-CS gauge theory due to noncommutativity of spatial coordinates is proposed. We carry out the one-loop renormalization and a noncommutative correction for the Chern-Simons coefficient is obtained. Finally it is found that this new correction depends of the noncommutative parameter in an analytic form.

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“…The resulting noncommutative field theory is a natural setting to define the θ -deformation of Donaldson invariants and they are interpreted as a mapping between the ChevalleyEilenberg homology of noncommutative spacetime and the Chevalley-Eilenberg cohomology of noncommutative moduli of instantons. In the process one can find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons [54].…”

Section: Noncommutative Field Theoriesmentioning

confidence: 99%