On a class of topological quantum field theories in three-dimensions

We investigate the Chung-Fukuma-Shapere theory, or Kuperberg theory, of three-dimensional lattice topological field theory. We construct a functor which satisfies the Atiyah's axioms of topological quantum field theory by reformulating the theory as Turaev-Viro type state-sum theory on a triangulated manifold. The theory can also be extended to give a topological invariant of manifolds with boundary.Comment: 22 pages, LaTeX, 9 ps figures include

New Covariant Gauges in String Field Theory

A single-parameter family of covariant gauge fixing conditions in bosonic string field theory is proposed. It is a natural string field counterpart of the covariant gauge in the conventional gauge theory, which includes the Landau gauge as well as the Feynman (Siegel) gauge as special cases. The action in the Landau gauge is largely simplified in such a way that numerous component fields have no derivatives in their kinetic terms and appear in at most quadratic in the vertex.Comment: 24 page

Supersymmetric extended string field theory in NS^n sector and NS^{n-1}-R sector

We construct a class of quadratic gauge invariant actions for extended string fields defined on the tensor product of open superstring state space for multiple open string Neveu-Schwarz (NS) sectors with or without one Ramond (R) sector. The basic idea is the same as for the bosonic extended string field theory developed by the authors [arXiv:1309.3850]. The theory for NS^n sector and NS^{n-1}-R sector contains general n-th rank tensor fields and (n-1)-th rank spinor-tensor fields in the massless spectrum respectively. In principle, consistent gauge invariant actions for any generic type of 10-dimensional massive or massless tensor or spinor-tensor fields can be extracted from the theory. We discuss some simple examples of bosonic and fermionic massless actions.Comment: 25 page

On three-dimensional topological field theories constructed from Dω(G)D^\omega(G) for finite group

We investigate the 3d lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation \D{G} of the quantum double of a finite commutative group $G$ as the underlying Hopf algebra. It is suggested that Chung-Fukuma-Shapere partition function is related to that of Dijkgraaf-Witten by \zcfs = |\zdw|^2 when $G=\Z_{2N+1}$. For $G=\Z_{2N}$, such a relation does not hold.Comment: 13 pages, 3 PS figures include

Physical state representations and gauge fixing in string theory

We re-examine physical state representations in the covariant quantization of bosonic string. We especially consider one parameter family of gauge fixing conditions for the residual gauge symmetry due to null states (or BRST exact states), and obtain explicit representations of observable Hilbert space which include those of the DDF states. This analysis is aimed at giving a necessary ingredient for the complete gauge fixing procedures of covariant string field theory such as temporal or light-cone gauge.Comment: 16 page