One-loop structure of the U(1) gauge model on the truncated Heisenberg space

Burić, Maja; Nenadović, Luka; Prekrat, Dragan

doi:10.1140/epjc/s10052-016-4522-x

Cited by 6 publications

(5 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hoping to build on the GW model's success, [20,21] tried to adapt it to a gauge field on h tr . Still, after extensive treatment, we found nonrenormalizability lurking in the form of divergent nonlocal derivative counterterms [22]. Apart from the trivial vacuum, this model contains another, which breaks the translational invariance:…”

Section: Introductionmentioning

confidence: 84%

“…Additionally, we mean to revisit the GW-inspired gauge model [22] in the hope of uncovering the reverse effect: non-renormalizability due to retention of the stripe phase. After fixing the NC strength and scale, the model is left with only one adjustable parameter -the field strength coupling g. Its additional stripe-like vacuum (5) transforms into a trivial one for the infinite coupling, implying the phase diagram's possible structure: stripe phase for small g, disordered phase for large g.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

Prekrat

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We construct and analyze a phase diagram of a self-interacting matrix field coupled to curvature of the non-commutative truncated Heisenberg space. In the infinite size limit, the model reduces to the renormalizable Grosse-Wulkenhaar's. The curvature term is crucial to renormalization. When turned off, the triple point collapses into the origin as matrices grow larger. When turned on, the triple point shifts away proportionally to the coupling strength and matrix size. Coupling attenuation that renormalizes the Grosse-Wulkenhaar model cannot contain the shifting, and the translational symmetry-breaking stripe phase escapes to infinity, taking away the problematic UV/IR mixing.

show abstract

Section: Introductionmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

Prekrat

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The techniques of this paper should also be relevant in the gauge model on the truncated Heisenberg algebra [35], where one of the gauge field components is coupled to the curvature.…”

Section: Jhep01(2023)109 6 Conclusion and Discussionmentioning

confidence: 99%

Approximate treatment of noncommutative curvature in quartic matrix model

Prekrat

Ranković

Todorović-Vasović

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

We study a Hermitian matrix model with the standard quartic potential amended by a tr(RΦ2) term for fixed external matrix R. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model — a renormalizable noncommutative field theory. The extra term breaks the unitary symmetry of the action and leads, after perturbative calculation of the unitary integral, to an effective multitrace matrix model. Accompanying the analytical treatment of this multitrace approximation, we also study the model numerically by Monte Carlo simulations. The phase structure of the model is investigated, and a modified phase diagram is identified. We observe a shift of the transition line between the 1-cut and 2-cut phases of the theory that is consistent with the previous numerical simulations and also with the removal of the noncommutative phase in the Grosse-Wulkenhaar model.

show abstract

“…This part is crucial in describing the asymmetric regime of the theory. It would also be interesting to consider the matrix model for the GW-inspired 𝑈 (1) gauge field theory [55], where the UV/IR-mixing seems to persist, and see what happens to the striped phase there. Finally, we have presented only the perturbative treatment of the curvature term in the GW model and we would like to entertain the possibility of treating it in a non-perturbative way.…”

Section: Discussionmentioning

confidence: 99%

Towards removal of striped phase in matrix model description of fuzzy field theories

Tekel,

Subjakova,

Prekrat

et al. 2023

Proceedings of Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2022)

View full text Add to dashboard Cite

The UV/IR-mixing phenomenon of non-commutative field theories is manifested by the existence of a non-local, striped phase in the scalar field theory, where the field does not oscillate around the same value in the whole space. We will consider modifications of the standard "kinetic term plus potential" actions for Hermitian matrix models which describe theories free of the UV/IR-mixing and discuss the expected receding of the striped phase in the phase diagram. We will present results for the case of the modified theory on the fuzzy sphere and for the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model on the plane.

show abstract

One-loop structure of the U(1) gauge model on the truncated Heisenberg space

Cited by 6 publications

References 45 publications

Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

Approximate treatment of noncommutative curvature in quartic matrix model

Towards removal of striped phase in matrix model description of fuzzy field theories

Contact Info

Product

Resources

About