Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in t', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.     

N = 4 supergravity theory with local SU(2) × SU(2) invariance

N = 4 supergravity theory has been formulated in two different equivalent forms, which may be expected to become inequivalent when the internal symmetry is gauged. The extension of the first form to include local SO(4) internal symmetry is known. In this paper the extension of the second form to local SU(2) × SU(2) invariance is given, and is indeed inequivalent to the first form. The second form is in general parity non-conserving, while both forms have scalar field potentials that are unbounded from below.     

Gauged N = 8 supergravity in five dimensions

We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6,R), specially SO(p, 6?p) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E₆₍₆₎ symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.     

N=4 conformal supergravity and irreducible superfields

Among irreducible N=4 superfields, into which can be decomposed a general N=4 scalar superfield, we select a superfield with 128 + 128 components which characterizes a conformai N=4 supercurrent. The obtained superfield is used in order to explicitly construct the linearized N = 4 conformai supergravity outside the mass shell in N = 4 superspace.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 83–87, September, 1989.     

Linearized N = 2 supergravity in terms of SU(2)-extended superfields

The linearized theory of N = 2 conformai supergravity is expressed in terms of a single irreducible SU(2)-extended superfield. In particular, in this way the origin of the N = 2 superconformal multiplet is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 5, pp. 93–95, May, 1986.     

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.     

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.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

Maximal-helicity-violating n-point one-loop amplitude in N=4 supergravity

We propose an explicit formula for the n-point maximal-helicity-violating one-loop amplitude in a N=4 supergravity theory. This formula is derived from the soft and collinear factorizations of the amplitude.     

N=1 Dilatation supergravity

The geometrical aspect of theN=1 dilatation supergravity is here studied from the point of view of the internal structure of matter. It is shown thatN=1 supergravity may be taken to have arisen from the internal helicity of hadrons and gives rise to a torsion term in the gravitational action. This formalism is found to be in conformity with the chiral formalism of superfield developed by other authors.     

Linearized N=2 Poincaré supergravity in terms of SU(2)-extended superfields

Linearized Poincaré N=2 supergravity is presented in terms of SU(2)-extended superfields. Thus, the connection of SU(2)-extended superfields with the structure of auxiliary fields in N=2 supergravity is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 31–34, October, 1986.     

Cancellations beyond finiteness in N=8 supergravity at three loops

We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions no worse than that of N=4 super-Yang-Mills theory--a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of quantum gravity.