Scalar fields in a non-commutative space

14th Mexican Workshop on Particles and Fields

Bietenholz, Wolfgang^1 ; Hofheinz, Frank^2 ; Mejía-Díaz, Héctor^1 ; Panero, Marco^3

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, México, Distrito Federal

C.P. 04510, Mexico^1

Institute of Radiopharmaceutical Cancer Research, Helmholtz-Zentrum Dresden-Rossendorf, Germany^2

Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, Madrid

28049, Spain^3

关键词: Dispersion relations;    Hermitian matrices;    Non-commutative space;    Numerical results;    Scaling limits;    Stripe pattern;    Striped phase;    Translation symmetry;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/651/1/012003/pdf
DOI  :  10.1088/1742-6596/651/1/012003

来源: IOP

【 摘 要 】

We discuss the λφ4 model in 2- and 3-dimensional non-commutative spaces. The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations. The numerical results reveal a phase where stripe patterns dominate. In d = 3 we show that in this phase the dispersion relation is deformed in the IR regime, in agreement with the property of UV/IR mixing. This "striped phase" also occurs in d = 2. For both dimensions we provide evidence that it persists in the simultaneous limit to the continuum and to infinite volume ("Double Scaling Limit"). This implies the spontaneous breaking of translation symmetry.