Geometry of 4d Simplicial Quantum Gravity with a U(1) Gauge Field
  The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the curvature distribution of S^4 space shows an inflated geometry with homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the scalar curvature geometry of the space is measured. 
H.S.Egawa, S.Horata and T.Yukawa