Vector field effective action in the open superstring theory

Using a path integral technique we find a closed expression (to all orders in α′) for the abelian, constant field strenght limit of the (tree) effective action for the massless vector field in the open superstring theory. The result is a modification of the Born-Infeld action found in the Bose string theory case. One-loop correction to the effective action is computed and shown to be finite if the gauge group is SO(32). It is demonstrated how the on-shell superstring scattering amplitudes can be calculated in the path-integral approach. We determine the leading (O(α') and O(α′²)) terms in the full non-abelian effective action starting from the known results for the 3-point and 4-point amplitudes. We find that because of the equivalence theorem the coefficients of some of the invariant structures in the effective lagrangian cannot be fixed from the S-matrix. In the path integral approach this ambiguity manifests itself as a 2d renormalization scheme (and Weyl gauge choice) ambiguity. We also discuss the leading terms in the gravitational effective actions in the closed (super) string theories and point out that whether or not the R² terms form the “Gauss-Bonnet” combination depends on choice of a renormalization (massless exchange subtraction) scheme.     

Order α′3 effective action of superstring theory

We calculate the on-shell effective action which generates toO(α^′3) the tree-level stringS-matrix elements with external graviton and dilaton fields.     

Elliptic index and superstring effective actions

Certain N = 1 supersymmetric string one-loop effective actions can be obtained directly from the path integral. As the computation is essentially the same as the one leading to the index of the Dirac-Ramond operator, they are determined by the gauge and gravitational anomaly structure of the theory. Specifically, we calculate the four-point effective action in ten dimensions, the corrections to the kinetic terms in d = 6 (including auxiliary fields) and the Fayet-Iliopoulos D-term in d = 4. We also compute the β-function of four-dimensional N = 2 theories from the elliptic genus in d = 6. Furthermore, we derive supersymmetry Ward type identities in terms of Kac-Moody characters, relating parity conserving with parity violating amplitudes.     

Duality symmetry of the p-form effective action and supertrace of the twisted de Rham complex

We consider quantum p-form fields interacting with a background dilaton. We calculate the variation with respect to the dilaton of a difference of the effective actions in the models related by a duality transformation. We show that this variation is defined essentially by the supertrace of the twisted de Rham complex. The supertrace is then evaluated on a manifold of an arbitrary dimension, with or without boundary.     

One-loop correction of the tachyon action in boundary superstring field theory

We compute one-loop correction to the string field theory action of the tachyon for unstable D-branes in the framework of the boundary superstring field theory. We would expect that the one-loop correction comes from the partition function of the two-dimensional worldsheet theory on the annulus. The annulus correction suggests that the genus expansion is, somehow, governed by the effective string coupling defined in terms of the tachyon λ=g_sexp(−T²/4).     

The Born-Infeld action from conformal invariance of the open superstring

We show that the one-loop approximation to sigma-model perturbation theory for the open-superstring leads to the low-energy effective action of Born-Infeld for the gauge field coupled to the ends of the string. Thus the bosonic part of the low-energy open superstring effective action is just that of the open bosinic string. We also that these results are exact to all loop orders of sigma-model perturbation theory.     

Supermanifold cohomology and the Wess-Zumino term of the covariant superstring action

The cohomology theory of supermanifolds is developed. Its basic properties are established and simple examples given. The Wess-Zumino term in the Green-Schwarz covariant superstring action is interpreted as a nontrivial class in the supersymmetric cohomology of flat superspace. A quotient supermanifold with nontrivial topology reflecting this class is constructed. It is shown that there is no topological quantization condition for the coefficient of the Wess-Zumino term. The superstring differs from conventional sigma models in this respect because its action is Grassmann-valued and its group manifold (superspace) is noncompact.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073)     

N=1 supersymmetric truncations and the superstring low-energy effective theory

The question of discarding heavy fields in N=1 supersymmetric theories is analyzed. The analysis is applied to the compactification of the E₈ × E₈ superstring.     

Purely cubic action for superstring field via noncommutative supergeometry

Witten's superstring field action is shown to be obtained from a purely cubic action by using noncommutative supergeometry.     

Tensor analysis on conformal supergeometry and the ghost action of the superstring

The orthogonal decomposition technique is extended to the physical and ghost tensor superfields on the two-dimensional conformal supergeometry. This method makes the meaning of the superfield functional integral clearer. The form of the ghost action of the superstring in the superspace formulation is discussed on this basis.     

Relation between anomaly in type-I superstring and anomaly in its effective theory

We explicitly calculate the hexagon and heptagon (covariant) gauge anomaly including the precise numerical coefficients in type-I open superstring. The calculation is performed by using the Pauli-Villars regularization on the basis of the stringy Ward identity, which is an assumption weaker than the cancelled propagator argument. We show that the anomalies in the effective theory are realized as the zero slope limit (α^′→0) of the string anomalies in a very non-trivial way in the present calculational scheme. This non-trivial realization in higher point (n≧8) anomalies is also discussed.