Fermionic String Theory Research Articles

Open string model building

Consistency conditions of open string theories, which can be a powerful tool in open string model building, are proposed. By making use of these conditions and assuming a simple prescription for the Chan-Paton factors, open string theories in several backgrounds are studied. We show that (i) there exist a large number of consistent bosonic open string theories on Z 2 orbifolds, (ii) SO(32) type I superstring is the unique consistent model among fermionic string theories on the ten-dimensional flat Minkowski space, and (iii) with our prescription for the Chan-Paton factors, there exist no consistent open superstring theories on (six-dimensional Minkowski space-time) ⊗ (Z 2 orbifold).

The exact equivalence of Chern-Simons theory with fermionic string theory

We show that non-abelian Chern-Simons gauge theory in three dimensions is an exact soluble system. For S 3 and non-simply connected manifolds which are homology three-spheres we determine the quantum theory in terms of a non-critical fermionic string theory.

ON THE MULTILOOP CONTRIBUTION TO THE STRING THEORY

The supermoduli space and the measure on this space arising from fermionic string theory are studied. Analytic properties of this measure are analyzed. Our considerations, combined with previous results by Voronov, give an expression of string measure through analytic superfields and their zeros. The behavior of measure in the vicinity of the boundary of moduli space is studied on the base of this expression.

Superalgebras, symplectic bosons and the Sugawara construction

New representations of affine Lie algebras are constructed using symplectic bosons of the sort that occur naturally in the BRST treatment of fermionic string theories. These representations are shown to have analogous properties to the current algebra representations in terms of free fermion fields, though they do not act in a positive space. In particular, the condition for the Sugawara construction of the Virasoro algebra to equal the free one is the existence of a superalgebra with a quadratic Casimir operator, paralleling the symmetric space theorem for fermionic field constructions. Both results are seen to be particular cases of a more general super-symmetric space theorem, which arises from considering an affinisation of the superalgebras. These algebras are realised in terms of free fermions and symplectic bosons and lead to a super-Sugawara construction of the Virasoro algebra. The conditions for this to equal a Virasoro algebra obtained from the free fields are provided by the super-symmetric space theorem.

Anomalies, characters and strings

One-loop modular invariant heterotic and type II closed string theories are proved to be anomaly free, apart from terms proportional to Tr F 2 − Tr R 2. It is shown why this conclusion holds with remarkable generality for any conceivable fermionic string theory, regardless even of conformal invariance. A detailed discussion is given of the modular properties of character valued partition functions, upon which the proof is based. The fact that Tr F 2 − Tr R 2 terms remain in the fermionic contribution to the anomaly is shown to be a consequence of Quille's holomorphic anomaly.

Ising model of a randomly triangulated random surface as a definition of fermionic string theory

Fermionic degrees of freedom are added to randomly triangulated planar random surfaces. It is shown that the Ising model on a fixed graph is equivalent to a certain Majorana fermion theory on the dual graph.

Superspace geometry of fermionic strings

We calculate the effective action in Polyakov's fermionic-string theory in a manifestly supersymmetric formalism, including the effects of string boundaries. Supersymmetry causes divergence cancellations such that no Liouville interaction term is generated by renormalization of the string fields. For open surfaces, supersymmetry is spontaneously broken by the presence of the boundary, leading to a linear divergence proportional to the length of the boundary.

The [formula omitted] potential and the migdal string

We show that the universal, long-ranged 1 R correction to the linear potential is unable to distinguish between the fermionic string theory recently advocated by Migdal and more standard string pictures.