Quantum effective potential for U(1) fields onS2L×S2L

Castro-Villarreal, Pavel; Delgadillo-Blando, Rodrigo; Ydri, Badis

doi:10.1088/1126-6708/2005/09/066

Cited by 25 publications

(40 citation statements)

References 33 publications

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“…Extension of this analysis to higher gauge groups U(n) and to 4−dimensions will be reported elsewhere [12].…”

Section: Resultsmentioning

confidence: 99%

“…As a consequence it is easy to check that the contribution of the first sum will indeed go to zero in the limit since Λ << L. In the large L limit one can therefore conclude that the full sum will be dominated by the second term corresponding to high internal momenta l 1 and l 2 , viz 12) where for convenience we have also made the following change of variables l = 1…”

Section: The Continuum Limitmentioning

confidence: 91%

“…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%

“…The first term in (4.7) gives the full tree-level action of the gauge field A a . This reads 12) where…”

Section: The U (1) Theorymentioning

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

Self Cite

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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“…Extension of this analysis to higher gauge groups U(n) and to 4−dimensions will be reported elsewhere [12].…”

Section: Resultsmentioning

confidence: 99%

Section: The Continuum Limitmentioning

confidence: 91%

Section: Scalar Actionmentioning

confidence: 99%

“…The first term in (4.7) gives the full tree-level action of the gauge field A a . This reads 12) where…”

Section: The U (1) Theorymentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

106

View full text Add to dashboard Cite

show abstract

“…This limit was investigated perturbatively in [14,17] for scalar and Yang-Mills field theories respectively. In 4−dimensions we should instead consider Cartesian products of the fuzzy sphere S 2 N [15], fuzzy CP 2 N [18] or fuzzy S 4 [19]. An alternative way of regularizing gauge theories on the Moyal-Weyl NC space is based on the matrix model formulation of the twisted Eguchi-Kawai model.…”

Section: Jhep11(2006)016mentioning

confidence: 99%

Monte Carlo simulation of a NC gauge theory on the fuzzy sphere

O’Connor¹,

Ydri²

2006

J. High Energy Phys.

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We find using Monte Carlo simulation the phase structure of noncommutative U (1) gauge theory in two dimensions with the fuzzy sphere S 2 N as a non-perturbative regulator. There are three phases of the model. i) A matrix phase where the theory is essentially SU (N ) Yang-Mills reduced to zero dimension . ii) A weak coupling fuzzy sphere phase with constant specific heat and iii) A strong coupling fuzzy sphere phase with non-constant specific heat. The order parameter distinguishing the matrix phase from the sphere phase is the radius of the fuzzy sphere. The three phases meet at a triple point. We also give the theoretical one-loop and 1 N expansion predictions for the transition lines which are in good agreement with the numerical data. A Monte Carlo measurement of the triple point is also given.

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Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in N = 4 $$ \mathcal{N}=4 $$ SYM and matrix models

Steinacker

Zahn

2015

J. High Energ. Phys.

104

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We find new vacuum solutions of N = 4 super-Yang-Mills with totally antisymmetric cubic soft SUSY breaking terms, or equivalently solutions of the IKKT matrix model of type R 4 θ × K N with flux terms. The solutions can be understood in terms of 4-and 6-dimensional fuzzy branes K N in extra dimensions, describing self-intersecting projections of compact flag manifolds of SU(3). The 6-dimensional solutions provide a 6-fold covering of the internal space near the origin, while the 4-dimensional branes have a triple self-intersection spanning all 6 internal directions. The solutions have lower energy than the trivial vacuum, and we prove that there are no negative modes. The massless modes are identified explicitly. In particular there are chiral fermionic zero modes, linking the coincident sheets with opposite flux at the origin. They have a Z 3 family symmetry, originating from the Weyl group rotations.

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Quantum effective potential for U(1) fields onS²_L×S²_L

Cited by 25 publications

References 33 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

Monte Carlo simulation of a NC gauge theory on the fuzzy sphere

Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in N = 4 $$ \mathcal{N}=4 $$ SYM and matrix models

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