On superspace supergravity in ten dimensions

Off-shell N=1, d=10 supergravity splits into a (128+128)-component multiplet and two scalar superfields. A concise formulation of the superspace contraints corresponding to the (128+128)-multiplet is given and the incorporation of the dimension - 6 scalar superfield discussed at the linearized level. The second scalar superfield, whose leading component is the physical dilaton field, may be regarded as being external to the superspace geometry. An action for the full non-linear theory is proposed.     

Anomaly-free supergravity and super-Yang-Mills theories in ten dimensions

We formulate in ten dimensions a supergravity theory coupled to a super-Yang-Mills theory through the Green-Schwarz ansatz, which ensures chiral anomaly cancellation. The formulation is obtained by fixing suitable constraints in the superspace and solving the Bianchi identities. In this way we obtain the whole set of equations of motion. They are characterized by highly non-polynomial expressions, when expressed only in terms of the physical superfields. We discuss the problem of the massive modes appearing in some of these equations.     

Massive N = 2a supergravity in ten dimensions

A new version of the non-chiral N = 2a supergravity in ten dimensions is obtained, in which the two-index tensor field of the theory “eats” the single vector field and acquires a mass in a Higgs-type mechanism. The new theory, although it contains no fundamental vectors, bears many formal resemblances to gauged supergravities (in particular, the recently constructed F(4) theory in six dimensions). The scalar potential has no extrema, but nevertheless the classical equations of motion admit a wide variety of spontaneous compactifications, many to four dimensions.     

Maximal gauged supergravity in three dimensions

We construct maximally supersymmetric gauged N = 16 supergravity in three dimensions, thereby obtaining an entirely new class of anti--de Sitter supergravities. These models apparently cannot be derived from any known higher-dimensional theory and point to the existence of a new type of supergravity beyond D = 11. One of their noteworthy features is a non-Abelian generalization of the duality between scalar and vector fields in three dimensions. Among the possible gauge groups, SO(8) x SO(8) is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as F(4(-20)) x G2.     

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.     

Conformal supergravity tree amplitudes from open twistor string theory

We display the vertex operators for all states in the conformal supergravity sector of the twistor string, as outlined by Berkovits and Witten. These include ‘dipole’ states, which are pairs of supergravitons that do not diagonalize the translation generators. We use canonical quantization of the open string version of Berkovits, and compute N-point tree level scattering amplitudes for gravitons, gluons and scalars. We reproduce the Berkovits–Witten formula for maximal helicity violating (MHV) amplitudes (which they derived using path integrals), and extend their results to the dipole pairs. We compare these trees with those of Einstein gravity field theory.     

N = 8 supergravity in various dimensions and the implications for four dimensions

The possibilities for constructing new spontaneously broken N = 8 supergravity theories in four dimensions by applying the generalized dimensional reduction method to symmetrical theories in higher dimensions are explored.     

The structure ofN=16 supergravity in two dimensions

We extend the previously constructed linear system forN=16 supergravity in two dimensions by including the unphysical gravitino degrees of freedom. This theory has a residualN=16 superconformal invariance that can be bosonized to localE ₉ transformations. The modifications to the linear system described here suggest a further extension to an infinite hierarchy of fields and associated gauge transformations related toE ₉.On leave of absence from: Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139, USAWork supported in part by National Science Foundation Grant #85-07109     

Conformal blocks for arbitrary spins in two dimensions

Conformal blocks for the finite dimension conformal group SO(2,2)$\mathit{SO}(2,2)$ for four point functions for fields with arbitrary spins in two dimensions are obtained by evaluating an appropriate integral. The results are just products of hypergeometric functions of the conformally invariant cross ratios formed from the four complex coordinates. Results for scalars previously obtained are a special case. Applications to four point functions involving the energy momentum tensor are discussed.     

Conformal and poincaré tensor calculi in N=1 supergravity

We present the superconformal tensor calculus for N=1 supergravity in a complete form; irreducible multiplets, their multiplication and embedding formulae and invariant action formulae. It is further clarified in detail how the various versions of N=1 Poincaré supergravity (i.e. with different sets of auxiliary fields) are reproduced from the unique superconformal theory. The tensor calculi for all the known versions of Poincaré supergravity are derived explicitly.     

Noncompact gaugings and critical points of maximal supergravity in seven dimensions

From the recently obtained SO(5)-gauged maximal d = 7 supergravity, we derive further noncompact SO(4, 1) and SO(3, 2) gaugings. Their potentials have no critical points. The SO(5) potential has two critical points with SO(5) and SO(4) symmetry, respectively. The former is stable under small and large fluctuations, the latter is unstable and breaks all supersymmetries.     

Conformal field theories near a boundary in general dimensions

The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions d. Calculations of the universal function of a conformal invariant ξ which appears in the two-point function of scalar operators in conformally invariant theories with a plane boundary are undertaken to first order in the ge = 4 − d expansion for the operator φ² in φ⁴ theory. The form for the associated functions of ξ for the two-point functions for the basic field φ^α and the auxiliary field λ in the N → ∞ limit of the O(N) nonlinear sigma model for any d in the range 2 < d < 4 are also rederived. These results are obtained by integrating the two-point functions over planes parallel to the boundary, defining a restricted two-point function which may be obtained more simply. Assuming conformal invariance this transformation can be inverted to recover the full two-point function. Consistency of the results is checked by considering the limit d → 4 and also by analysis of the operator product expansions for φ^αφ^β and λλ. Using this method the form of the two-point function for the energy-momentum tensor in the conformal O(N) model with a plane boundary is also found. General results for the sum of the contributions of all derivative operators appearing in the operator product expansion, and also in a corresponding boundary operator expansion, to the two-point functions are also derived making essential use of conformal invariance.