Stripes from (non-commutative) stars

Abstract

We show that lattice regularization of noncommutative field theories can be used to study non-perturbative vacuum phases. Specifically we provide evidence for the existence of a striped phase in two-dimensional noncommutative scalar field theory.

Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

“…This type of scaling seems to be generic to the matrix regularization of noncommutative field theories [26,30]. In particular, the continuum limits of the lattice derived matrix models of noncommutative field theory seem to be most naturally associated with the trivial Gaussian fixed point of the corresponding commutative theory [34,35]. Notice, however, that if we replace the bare coupling g by the renormalized coupling constant Λ 2n−4 g, then the function Λ −2 W (Λ −2 ξ) has a more complicated form reflecting the interacting nature of the quantum field theory, provided we simply interpret Λ as the finite mass scale set by the magnetic field.…”

Lattice perturbation theory in noncommutative geometry and parity anomaly in 3d noncommutative QED

“…In the literature it is common to start from a finite-N matrix model, which is then shown to be equivalent to the lattice formulation of a noncommutative field theory. Indeed, the matrix model representation has proven useful for numerical analyses [15,16,18,20]. Here we will work directly with the lattice formulation and derive the Feynman rules, which are used in the perturbative evaluation of the effective action induced by fermions.…”

“…In the case where ψ(x) transforms in the fundamental representation 18) they are given respectively by…”

“…There the same theory was shown to have an intriguing infrared property which may be described as the Aharonov-Bohm effect with the magnetic field identified with the inverse noncommutativity parameter. The lattice formulation has also been used to explore the phase diagram of noncommutative scalar field theories [16,18], which is expected to be richer than in the commutative case, as indicated by a self-consistent Hartree approximation [19]. In particular, as conjectured by Ref.…”

Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

“…Other models by using the Dirac-Kähler fermion without modified Leibniz rule possess the partial twisted supersymmetries. These models was investigated in [36][37][38][39][40][41][42][43][44][45][46]. In the recent development of lattice SUSY, there are matrix formulations on which we impose Z N orbifold conditions [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63].…”