Quantized gauge theory on the fuzzy sphere as random matrix model

Steinacker, Harold

doi:10.1016/j.nuclphysb.2003.12.005

Cited by 140 publications

(283 citation statements)

References 38 publications

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“…In other words suppressing the normal component of the gauge field by giving it a large mass allowed us to suppress in the limit the contribution of the tangential field to the tadpole and to the 4−vertex correction of the vacuum polarization tensor. By the requirement of gauge-invariance this suppression will also occur in the other contributions to the vacuum polarization tensor and as consequence the large mass of the scalar field regulates effectively the UV-IR mixing which is consistent with [8].…”

Section: The Quadratic Effective Action In the Limit M−→∞supporting

confidence: 56%

“…In fact (3.11) is the correct definition of the normal scalar field on the fuzzy sphere which is only motivated by gauge invariance. Following [8] we incorporate the constraint (3.11) into the theory by adding the following scalar action 12) to (3.3) where M is a large mass. This term in the continuum theory changes the mass term of the Higgs particle appearing in (3.6) from √ 2 to 2(1 + 2M 2 ) and hence in the large M limit the normal scalar field simply decouples.…”

Section: Scalar Actionmentioning

confidence: 99%

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A gauge invariant UV–IR mixing and the corresponding phase transition for fields on the fuzzy sphere

Castro-Villarreal¹,

Delgadillo-Blando²,

Ydri³

2005

Nuclear Physics B

106

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From a string theory point of view the most natural gauge action on the fuzzy sphere S 2 L is the Alekseev-Recknagel-Schomerus action which is a particular combination of the YangMills action and the Chern-Simons term . The differential calculus on the fuzzy sphere is 3−dimensional and thus the field content of this model consists of a 2-dimensional gauge field together with a scalar fluctuation normal to the sphere . For U (1) gauge theory we compute the quadratic effective action and shows explicitly that the tadpole diagrams and the vacuum polarization tensor contain a gauge-invariant UV-IR mixing in the continuum limit L−→∞ where L is the matrix size of the fuzzy sphere. In other words the quantum U (1) effective action does not vanish in the commutative limit and a noncommutative anomaly survives . We compute the scalar effective potential and prove the gauge-fixingindependence of the limiting model L = ∞ and then show explicitly that the one-loop result predicts a first order phase transition which was observed recently in simulation . The one-loop result for the U (1) theory is exact in this limit . It is also argued that if we add a large mass term for the scalar mode the UV-IR mixing will be completely removed from the gauge sector . It is found in this case to be confined to the scalar sector only. This is in accordance with the large L analysis of the model . Finally we show that the phase transition becomes harder to reach starting from small couplings when we increase M .

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Section: The Quadratic Effective Action In the Limit M−→∞supporting

confidence: 56%

Section: Scalar Actionmentioning

confidence: 99%

A gauge invariant UV–IR mixing and the corresponding phase transition for fields on the fuzzy sphere

Castro-Villarreal¹,

Delgadillo-Blando²,

Ydri³

2005

Nuclear Physics B

106

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show abstract

“…On the other hand, a fuzzy space description for gauge theory was studied in some papers, including [65,66,67,68,69,70,71,72,73,74,75,76,58].…”

Section: General Formalism and Theoretical Predictionsmentioning

confidence: 99%

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Panero¹

2006

SIGMA

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Abstract. We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.

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“…By using the modular transformation properties 20) it is possible to cast the string representation (5.8,5.9) in the weak-coupling regime λ ≪ 1 where the instanton expansion of the gauge theory is appropriate. It was argued in [48] that the contributions are of the generic form…”

Section: Gross-taylor Series On the Torusmentioning

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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Quantized gauge theory on the fuzzy sphere as random matrix model

Cited by 140 publications

References 38 publications

A gauge invariant UV–IR mixing and the corresponding phase transition for fields on the fuzzy sphere

A gauge invariant UV–IR mixing and the corresponding phase transition for fields on the fuzzy sphere

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Instantons, fluxons, and open gauge string theory

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