Scalar fields in a non-commutative space

Abstract

We discuss the lambda phi**4 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.

15 pages, LaTex, 13 figures, 1 table, talk presented at the XIV Mexican Workshop on Particles and Fields, Oaxaca, November 2013

References in corpus (5)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Stripes from (noncommutative) stars
• Nonuniform symmetry breaking in noncommutative $\lambda {\Phi }^4$ theory
• Simulating non-commutative field theory
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions

Cited by in corpus (4)

• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• Approximate treatment of noncommutative curvature in quartic matrix model
• Non-commutativity in polar coordinates
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature