Quantum gravity on the fuzzy sphere

Abstract: We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2\imath\lambda_p \epsilon_{ijk}x_k$ modulo setting $\sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant differential structure. Metrics are given by symmetric 3×3 matrices g and we show that for each metric there is a unique quantum Levi-Civita connection with constant coefficients, with scalar curvature $\frac{1}{2}({\rm Tr}(g^2)-\frac{1}{2}{\rm Tr}(g)^2)/\det(g)$. As an application, we construct Euclidean quantum gravity on the fuzzy unit sphere. We also calculate the charge 1 monopole for the 3D differential structure. Joint work with E. Lira Torres.

general relativity and quantum cosmologyHEP - theorymathematical physicsquantum algebra

Audience: researchers in the topic

Comments: Livestream platform: WEBEX

Mathematical Physics Seminar

Series comments: Description: Noncommutative geometry, field theory, gravity.