Heterotic Sigma Model Research Articles

Chiral gauged WZNW models and heterotic string backgrounds

We construct new heterotic string backgrounds which are analogous to superstring solutions corresponding to coset models but are not simply the “embeddings” of the latter. They are described by the (1,0) supersymmetric extension of the G/H chiral gauged WZNW models. The “chiral gauged” WZNW action differs from the standard gauged WZNW action by the absence of the AĀ-term (and thus is not gauge invariant in the usual sense) but can still be expressed as a combination of WZNW actions and is conformally invariant. We explain a close relation between gauged and chiral gauged WZNW models and prove that in the case of the abelian H the G/H chiral gauged theory is equivalent to a particular (G × H)/H gauged WZNW theory. In contrast to the gauged WZNW model, the chiral gauged one admits a (1,0) supersymmetric extension which is consistent at the quantum level. Integrating out the 2d gauge field we determine the exact (in α′) form of the couplings of the corresponding heterotic sigma model. While in the bosonic (superstring) cases all the fields depend (do not depend) nontrivially on α′ here the metric receives only one O(α′) correction while the antisymmetric tensor and the dilaton remain semiclassical. As a simplest example, we discuss the basic D = 3 solution which is the heterotic string counterpart of the “black string” SL(2, R ) × R / R background.

Weyl invariance of the Green-Schwarz heterotic sigma model

Weyl invariance at one loop is proven for the heterotic non-linear sigma model coupled to curved superspace with non-trivial fermionic and bosonic background fields. A general formula is given relating the Weyl anomaly to the sigma model β-functions at arbitrary sigma-model loop order. The Weyl anomaly is also considered in the presence of Yang-Mills backgrounds.

THE LORENTZ CHERN-SIMONS FORM IN HETEROTIC GREEN-SCHWARTZ SIGMA MODELS

By studying the 1-loop effective action of the heterotic Green-Schwartz sigma model, we identify the only source of anomaly in the target local Lorentz symmetry, and verify that it is canceled by the inclusion of a Lorentz Chern-Simons three-form in the definition of the supergravity field HABC.

NON MINIMAL ANOMALY FREE D=10, N=1 SUGRA-SYM AND FOUR-GRAVITON SUPERSTRING AMPLITUDES

A class of non minimal extensions of anomaly free D=10, N=1SUGRA—SYM, formulated in superspace, is proposed. The new models are obtained modifying suitably standard superspace constraints of the minimal one. It is shown that the proposed models are likely to accommodate the effective four-bosons superstring amplitudes. The relation existing between consistently quantized heterotic string sigma models and the consistency of our construction is exhibited.

The effect of gauge and Lorentz anomalies on the beta functions of heterotic sigma models

We compute the one-loop gauge and Lorentz anomalies as well as the gauge and Lorentz variant parts of the two-loop β-functions of heterotic type σ-models. The method used in the computation preserves the (1,0) supersymmetry manifest. We discuss the conjectured mechanism for absorbing the gauge and Lorentz variant parts of the two-loop β-functions by redefinition of the torsion. We show that this mechanism works at two loops, provided that the one-loop β-functions vanish.

The heterotic sigma model in the presence of background gauge fields. Three-loop results

The covariant part of the β-functions for the heterotic σ-model in the presence of background gauge fields is calculated up to three-loop order. The equations β=0 are shown to coincide with the equations of motion derived from an effective space-time action. This effective action has been obtained previously via the string S-matrix approach.