Joseph J. Atick

String calculation of fayet-iliopoulos D-terms in arbitrary supersymmetric compactifications☆

We calculate the Fayet-Iliopoulos D-terms generated at one loop for the heterotic string in any background which preserves four-dimensional space-time supersymmetry and maintains (2,0) world-sheet superconformal invariance. Although our calculation is performed in the full string theory, the result can be evaluated entirely in terms of properties of the massless spectrum. Furthermore it agrees with the result of a computation in the four-dimensional effective field theory using a stringy regularization. We also check our general result through a more explicit calculation in an orbifold background.

Spin field correlators on an arbitrary genus Riemann surface and non-renormalization theorems in string theories☆

Abstract We calculate the n -point correlation functions of spin fields on an arbitrary genus Riemann surface. We also calculate the corresponding correlators for the spin fields associated with the local supersymmetry ghosts using a specific ansatz for screening the background ghost charge. Using these results we show by explicit calculation that to all orders in the string perturbation theory all n -point amplitudes involving massless fields in the superstring and the heterotic string theory vanish identically for 0 ⩽ n ⩽ 3.

Covariant one-loop fermion emission amplitudes in closed string theories

We calculate the 2 fermion-2 boson and the 4 fermion scattering amplitudes at one loop in the NSR formulation of the heterotic and type II superstring theories using the covariant fermion emission vertex. The results are shown to agree with well known amplitudes calculated in the light-cone gauge in the Green-Schwarz formulation. The agreement of the 4-fermion amplitude entails the use of a new ϑ-function identity which we also prove.

Correlation Functions of Spin Operators on a Torus

An expression for the arbitrary n-point correlation function of SO(2) spin operators on a torus is derived. From this expression one can calculate the n-point correlation function of any SO(2N) spin operators. Application of our results to the calculation of one-loop scattering amplitudes involving SO(16) and SO(10) spin fields in superstring theories is also given.

Superstring propagation in curved superspace in the presence of background super Yang-Mills fields

Abstract A gauge invariant action is presented which describes the propagation of the superstring in curved superspace in the presence of background super Yang-Mills fields. It is shown that this action posseses the local fermionic world-sheet symmetry needed for a consistent coupling of the string to background fields. Some other aspects of the superspace non-linear σ-model described by this action are also discussed.

Multi-loop twist field correlation functions for ZN orbifolds

Abstract We calculate the correlation functions of bosonic twist fields for Z N orbifolds on Riemann surfaces of arbitrary genus.

Two Loop Dilaton Tadpole Induced by Fayet-Iliopoulos D-Terms In Compactified Heterotic String Theories*

We calculate the two-loop dilaton tadpole induced by Fayet-Iliopoulos D-terms in heterotic string theories compactified on arbitrary supersymmetry preserving backgrounds. The result turns out to be a total derivative in the moduli and hence receives contribution solely from the boundary of the moduli space. This contribution is shown to be proportional to the square of the coefficient of the one-loop Fayet-Iliopoulos D-term in agreement with what is expected from effective lagrangian considerations.

θ-Expansion and light-cone gauge fixing in curved superspace σ-models☆

Abstract A method for normal coordinate expansion of superspace σ-model actions is developed and used to obtain a covariant θ-expansion of the heterotic Green-Schwarz superstring in curved superspace. It is known that in the absence of background fermions the expansion terminates at order θ 2 in the light-cone gauge. An expression for the gauge-fixed action including background metric, torsion and Yang-Mills fields is given.

Two Loop Partition Function in (Compactified) Heterotic String Vacua

Two loop partition function for the heterotic string theory, compactified on any background preserving space-time supersymmetry at the string tree level, is explicitly calculated. This includes E 8 × E 8 or SO(32) heterotic string theory in ten dimensional flat space-time.