We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-Kähler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.

We propose the lattice version of BF gravity action whose partition function leads to the product of a particular form of 15-j symbol which corresponds to a 4-simplex. The action is explicitly constructed by lattice B field defined on triangles and link variables defined on dual links and is shown to be invariant under lattice local Lorentz transformation and Kalb-Ramond gauge transformation. We explicitly show that the partition function is Pachner move invariant and thus topological. The action includes the vanishing holonomy constraint which can be interpreted as a gauge fixing condition. This formulation of lattice BF theory can be generalized into arbitrary dimensions. = 2 2 J m 1 J m1 3 J m3 + J m 4 4 + J .In general any 3nj-symbols (n = 2, 3, 4, 5, ..) can be graphically represented by the closed trivalent graph. For example 6-j symbol can be decomposed into four 3-j symbols by the formula ,where the factor (−1) i (J i −m i ) can be understood as a sign factor coming from the invariant metric. The graphical presentation of the above 6-j symbol can be given 1 J