Field Theory on the q – Deformed Fuzzy Sphere
نویسندگان
چکیده
We study the q–deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus which is compatible with the star structure, study the integral, and find a canonical frame of one–forms. We then consider actions for scalar field theory, as well as for Yang–Mills and Chern–Simons–type gauge theories. The zero curvature condition is solved.
منابع مشابه
Quantum Field Theory on the q–deformed Fuzzy Sphere
We discuss the second quantization of scalar field theory on the q–deformed fuzzy sphere S2 q,N for q ∈ IR, using a path–integral approach. We find quantum field theories which are manifestly covariant under Uq(su(2)), have a smooth limit q → 1, and satisfy positivity and twisted bosonic symmetry properties. Using a Drinfeld twist, they are equivalent to ordinary but slightly “nonlocal” QFT’s o...
متن کاملAspects of the q–deformed Fuzzy Sphere
These notes are a short review of the q–deformed fuzzy sphere S2 q,N , which is a “finite” noncommutative 2–sphere covariant under the quantum group Uq(su(2)). We discuss its real structure, differential calculus and integration for both real q and q a phase, and show how actions for Yang–Mills and Chern–Simons–like gauge theories arise naturally. It is related to D-branes on the SU(2)k WZW mod...
متن کاملField Theory on the q–deformed Fuzzy Sphere II: Quantization
We study the second quantization of field theory on the q–deformed fuzzy sphere for q ∈ R. This is performed using a path integral over the modes, which generate a quasiassociative algebra. The resulting models have a manifest Uq(su(2)) symmetry with a smooth limit q → 1, and satisfy positivity and twisted bosonic symmetry properties. A systematic way to calculate n–point correlators in perturb...
متن کاملFuzzy Torus and q-Deformed Lie Algebra
It will be shown that the defining relations for fuzzy torus and deformed (squashed) sphere proposed by J. Arnlind, et al (hep-th/0602290) can be rewriten as a new algebra which contains q-deformed commutators. The quantum parameter q (|q| = 1) is a function of ~. It is shown that the q → 1 limit of the algebra with the parameter μ < 0 describes fuzzy S and that the squashed S with q 6= 1 and μ...
متن کاملDeformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-Sphere
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized by H(S,R). The fuzzy sphere is included as a special case parametrized by the integer two-cohomology class H(S,Z), which has finite number of degrees of fre...
متن کامل