Gauge invariant actions of free closed superstring field theories

A gauge invariant action of free N=1 closed superstring field theory is presented using BRS charges. This action is shown to take a similar form to that of open superstring. The N=2 closed superstring is also discussed.     

Superstring effects on D=4, N=1 supergravity

We give a lagrangian and supersymmetry transformation rules for the four-dimensional N=1 supergravity sector of superstring theories with their O(α′) corrections, obtained by the dimensional reduction á la Witten of the effective action of the ten-dimensional heterotic superstring. We also give general forms of O(α′ ″) corrections to supersymmetry transformation rules which arise through an axial vector superfield. Since our system is based on the ten-dimensional superstring without any auxiliary fields, our four-dimensional N=1 supergravity is free of auxiliary fields. Our point-field theory lagrangian is supposed to describe the mass-less fields in the untwisted sector of the ten-dimensional heterotic superstring propagating on orbifolds.     

N=2 superstrings in more than two dimensions?

For a string propagating in a Parisi-Sourlas superspace the critical dimension equals the difference in the number of positive-and negative-dimensional coordinates. In this way the dimension of the Minkowski subspace can be increased. Here we apply this to the N=2 superstring, with D_c=2 and find anomaly-free N=2 superstrings in all positive even dimensions. Nontrivial theories can be constructed from these N=2 theories by truncation: In a Parisi-Sourlas superspace with a ten-dimensional Minkowski subspace we find the N=1 NSR superstring, and with a four-dimensional Minkowski subspace we find an N=1 superstring, classically related to the D=10 NSR superstring by a canonical transformation.     

Quantum geometry of the covariant superstring with N = 1 global supersymmetry

The quantization of the superstring with N = 1 global supersymmetry is considered in the functional integral formalism. The term in the effective action defined by the conformal anomaly is calculated. It is shown that the effective action is determined not only by the intrinsic properties of the surface (i.e. by the metric h_αβ) but depends also on the way the surface is embedded in D-dimensional space (i.e. on the second quadratic form of the surface). The selfduality of N = 1 superstring theory with a Wess-Zumino term is pointed out.     

Superstring theory

Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(n) or Sp(2n) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D = 10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N = 4, D = 4 super Yang-Mills theory and SST II reduces to N = 8, D = 4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions.     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.     

New heterotic string theories in uncompactified dimensions < 10

It is shown that infinitely many heterotic string theories exist in uncompactified dimensions less than 10, that are one-loop finite (for massless external legs). Tachyons are removed by compactifying into tori (10 − d) and (26 −d) dimensions of the right-moving superstring and left-moving bosonic string sectors, respectively. The condition for modular invariance is shown to be equivalent to self-duality condition on even lorentzian lattices with (10 −d) and (26 −d) timelike and spacelike directions, respectively. The construction results in a (10 −d)(26 −d) parameter family of one-loop finite string theories. The zero mass sector of these theories for d = 4 and 6 correspond to N = 4 and 2 supergravity coupled to super Yang-Mills with many possible groups, some of which cannot be obtained by compactifying d = 10 heterotic string theory.     

Manifestly supersymmetric extensions of (curvature)2-terms in six-dimensional N = 2 supergravity

A systematic and manifestly supersymmetric procedure for supersymmetrization of general (curvature)²-terms in N = 2 supergravity in six dimensions (D = 6) is presented in superspace. The general form of new terms for the supersymmetrization in supertranslation rules is given. As a by-product, the superspace structure of quaternionic Kähler manifolds is elucidated. Our method is the D = 6 application of our previously established formulation for the D = 10, N = 1 supergravity with the O(α′) superstring corrections.     

N-Superstring vertex and the vertex operator for the emission of the superstring

The BRST invariant, supersymmetric N-string vertex which applies to both, the Neveu-Schwarz and Ramond sector of the superstring is formulated using the vertex operator for the emission of a superstring. It is shown that the N-superstring vertex thus obtained is cyclic symmetric when GSO projected on-shell states and operators for the external strings are applied. The constraint equations of this vertex and their singularity structure are examined and we show that this vertex also has the required property of a transition operator. We also give a proof of its BRST invariance and supersymmetry.     

Superstrings and the auxiliary field structure of supergravity

We construct the complete superfield of vertex operators corresponding to the four-dimensional N = 1 supergravity multiplet associated with the heterotic superstring. The supergravity fields are shown to consist of a graviton, gravitino, and two auxiliary fields and to form a new minimal supermultiplet. The role of R-invariance in new minimal supergravity is discussed.     

Analytic Tools to Brane Technology in N = 2 Gauge Theories with Matter

Exact solutions to the low-energy effective action (LEEA) of the four-dimensional N = 2 supersymmetric gauge theories are known to be obtained either by quantum field theory methods from S-duality in the Seiberg-Witten approach, or by the Type-IIA superstring/M-Theory methods of brane technology. After a brief review of the standard field-theoretical results for the N = 2 gauge (Seiberg-Witten) LEEA, we consider a field-theoretical derivation of the exact hypermultiplet LEEA by using the N = 2 harmonic superspace methods. We illustrate our techniques on a number of explicit examples. Our main purpose, however, is to discuss the existing analytical (calculational) support for the alternative methods of brane technology. We summarize known exact solutions to the eleven-dimensional and ten-dimensional type-IIA supergravities, which describe classical configurations of intersecting BPS branes with eight supercharges relevant to the non-perturbative N = 2 gauge theory with fundamental hypermultiplet matter. The crucial role of the M-Theory in providing a classical resolution of singularities in the ten-dimensional (Type-IIA superstring) brane picture, as well as the N = 2 extended supersymmetry in four dimensions, are made manifest. The two approaches to a derivation of the exact N = 2 gauge theory LEEA are thus seen to be complementary to each other and mutually dependent.     

Manifestly supersymmetric O(α′) superstring corrections in new D = 10, N = 1 supergravity Yang-Mills theory

A systematic procedure in superspace to derive the O(α′) tree-level superstring corrections to the new D = 10, N = 1 (dual) supergravity Yang-Mills system is established. All the tree-level O(α′) corrections in the closed supersymmetry transformation laws are presented explicitly. These O(α′) corrections are regarded as a generalization of “matter” couplings in D = 10, N = 1 supergravity. The advantage of the superspace approach, based on superspace Bianchi identities, in comparison with the component formulation is elucidated. This new method is applicable to all anomaly-free D ⩽ 10 non-maximal supergravity theories, which utilize the Green-Schwarz mechanism. It also provides a way of introducing general higher-order powers of curvature tensors in D ⩽ 10 supergravity theories.     

Symmetries and couplings in heterotic superconformal field theories

We discuss the symmetries of the superpotential in comfactified heterotic superstring theories formed from the product of minimal N = 2 superconformal field theories. It is shown how these symmetries can ensure flatness of the potential involving the moduli, and we derive new results (going beyond those obtained by superconformal techniques alone) for the flatness of the potential involving other massless fields.     

Nonrenormalizable superpotential in four-dimensional string models

A construction of an effective nonrenormalizable superpotential has been discussed within the approach of a four-dimensional heterotic superstring with free fermions on the world sheet. On the basis of N=2 superconformal theory, useful selection rules that take into account all global symmetries have been obtained within the formalism of covariant vertices and the ghost-picture-changing operation. The results have been applied to the model featuring the effective observable gauge group U(5)×U(3)_H, which includes the non-Abelian horizontal group and which describes (3+1) generation. The full superpotential of the model up to sixth order inclusive has been obtained, and its coupling constants have been calculated. The quark-lepton mass spectrum of the model has been discussed with allowance for contributions from nonrenormalizable terms.     

No renormalization of the N=1 supergravity theory derived from the heterotic string

We show that one-loop string effects do not alter the form of the leading terms in the low-energy effective ten-dimensional N=1 supergravity theory derived from the heterotic string. We extend this result to the four-dimensional N=1 supergravity theory obtained after compactification, showing in particular that its Kähler potential is not renormalized by string loop effects or by the exchange of Kaluza-Klein modes. We also demonstrate that the Kähler potential and the gauge kinetic function are not renormalized by one-loop string effects in a wide class of four-dimensional formulations of superstring theories.     

The inflationary universe in the gauged N=8 supergravity induced from a superstring

N=8 supergravity can contain a large negative cosmological constant. If this supergravity was induced on a four-dimensional space-time submanifold of a ten-dimensional space by a superstring moving in the latter manifold then there exists the possibility of a mutual cancellation of the constant mentioned and a positive one arising on the given submanifold due to quantum effects from the superstring. After this the evolution of the submanifold will depend essentially on its topological properties.     

Beta-functions and superstring compactifications

It is shown that quartic curvature modifications to the gravitational effective action derived from superstrings agree on Ricci-flat Kähler backgrounds with a recently-proposed four-loop counterterm in N = 2 Ricci-flat σ-models. These results seem to suggest that Calabi-Yau manifolds may not provide consistent compactifications of the superstring.     

Non-Abelian vortex in four dimensions as a critical superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional supersymmetric QCD with the gauge group, N _f = 4 quark flavors and the Fayet–Iliopoulos term. Under certain conditions, the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli, the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a twodimensional sigma model with the target space ?⁴ × Y ₆, where Y ₆ is a non-compact Calabi–Yau conifold. The closed string states that emerge in four dimensions (4D) are identified with hadrons of 4D bulk N= 2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole–monopole baryon of the 4D theory (at strong coupling).