Noncommutative network models

Noncommutative Linear Sigma Models

We examine noncommutative linear sigma models with U (N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that Nambu-Goldstone symmetry realization is inconsistent with continuum renormaliza-tion. Specifically we find no violation of Goldstone's theorem at one-loop for the U ...

Noncommutative Principal Chiral Models

Twisted Eguchi-Kawai reduced chiral models are shown to be formally equivalent to a U(1) noncommutative parent theory. To make contact with the continuum noncommutative theory, a double scaling large N limit for the reduced model is required. We show a possible limiting procedure, which we propose to investigate numerically. We also include some preliminary numerical results.

Geometric Models for Noncommutative Algebras

Comments on Noncommutative Sigma Models

We review the derivation of a noncommutative version of the nonlinear sigma model on CP and it’s soliton solutions for finite θ emphasizing the similarities it bears to the GMS scalar field theory. It is also shown that unlike the scalar theory, some care needs to be taken in defining the topological charge of BPS solitons of the theory due to nonvanishing surface terms in the energy functional...

Matrix models for noncommutative algebraic manifolds

We discuss the notion of matrix model, π : C(X) → MK(C(T )), for algebraic submanifolds of the free complex sphere, X ⊂ SN−1 C,+ . When K ∈ N is fixed there is a universal such model, which factorizes as π : C(X)→ C(X) ⊂MK(C(T )). We have X = Xclass and, under a mild assumption, inclusions X (1) ⊂ X ⊂ X ⊂ . . . ⊂ X. Our main results concern X, X, X, . . ., their relation with various half-class...