Structure of supergravity

It is shown how to construct actions and kinetic multiplets out of scalar multiplets of supergravity. The multiplets containing the scalar and the conformal tensor are obtained and yield the gauge actions of Einstein and Weyl supergravity. The complete supersymmetric R² and Bel-Robinson invariants are also obtained as well as general n-loop counterterms.     

Structure ofN=1 conformal and Poincaré supergravity in 1+1 and 2+1 dimensions

We discuss a component formalism ofN=1 supergravity theories in 2 and 3 spacetime dimensions. Starting from gauge theories of the superconformal group, we derive the tensor calculus for conformal and Poincaré supergravity theories. A supersymmetric extension of the non-trivial analog of Einstein's equation for 2 dimensions is given in terms of the scalar curvature multiplet.     

How chiral are type-II superstrings?

We study the type-II superstrings in four dimensions by studying vacua where massless chiral multiplets transform as complex representations of the non-abelian gauge group. We show that the gauge group can only be SU(3) and that such fields transform as 3 of SU(3). However, attempts to obtain the theory with N=1 supergravity fail. It turns out that the “different” constructions via asymmetric orbifolds give the same massless spectrum with necessarily N=2 supergravity.     

Supersymmetric gauge theories coupled to non-minimal and new minimal supergravity

The coupling of the various supergravity multiplets to gauge invariant theories is constructed using a chiral basis for curved superspace. It is shown thatR invariance is not required for such a construction.     

Structure of conformal supergravities in two dimensions

We examine constraints on curvatures inN=1 andN=2 conformal supergravities in two dimensions. We show that all curvatures should vanish in order that, the whole conformal supergravity algebra closes on all gauge fields. On the other hand we find some closed sub-algebra of the conformal supergravity one.     

Non-local Effects of Conformal Anomaly

It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein’s equations. The fact that Einstein’s general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein’s theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in \(D=4\) for both the \(C^2\) invariant and the Euler (Gauss–Bonnet) invariant can only be achieved for N-extended supergravity multiplets with \(N \ge 5\).     

Conformal supergravity in ten dimensions

We present the complete off-shell structure of conformal supergravity in ten dimensions. It is based on 128 + 128 degrees of freedom and its formulation requires differential constraints. We study how these constraints are resolved in four and five dimensions. Covariant conditions are given that restrict conformal supergravity to its on-shell Poincaré counterpart. In ten dimensions the relationship between the two theories has new and unusual aspects, which we explore in a variety of ways. We rewrite on-shell Poincaré supergravity in a superconformally invariant form, from which we deduce that its off-shell version must contain at least a scalar (chiral) multiplet. We analyze some aspects of the non-linear structure of the field representation based on the conformal fields combined with one scalar multiplet.     

(8,0) Locally supersymmetric sigma models with conformal invariance in two dimensions

The (8,0) conformal supergravity, and an action which describes its coupling to an arbitrary number of (8,0) scalar multiplets are constructed. The 64+64 components of the conformal supermultiplet occur as Lagrange multipliers which lead to differential and algebraic constraints on the fields of the scalar multiplets. Solving the algebraic constraints yields an (8,0) locally supersymmetric sigma model based on the manifold SO(8 + n,m)/SO(8)×SO(n,m), where n,m ⩾ 0.     

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.     

N=3 supersymmetry multiplets with vanishing trace anomaly: Building blocks of the N>3 supergravities

N?3 supergravity theories with vanishing one-loop trace anomaly may be constructed fron three basic N=3 multiplets, one of which contains an antisymmetric tensor gauge field. As an example we construct the N=4 theory and discuss its relationship to ten-dimensional supergravity.     

Linearized N = 2 superfield supergravity

We present the formulation of linearized SU(2) supergravity and U(2) conformal supergravity in terms of unconstrained N = 2 superfields: the gauge superfield, compensating superfields, gauge transformations, supertensors, actions and covariant derivatives.     

Heterotic σ-models and conformal supergravity in two dimensions

The (1, 0) and (2, 0) type heterotic σ-models with Wess-Zumino term are coupled to conformal supergravity in two dimensions. There are no new restrictions on the σ-model manifolds in addition to those which arise in the globally supersymmetric cases. In the (1, 0) case possible isometries of the scalar manifold are gauged. A derivation of d = 2 conformal supergravity based on the super Lie algebra OSp(2, N)⊕OSp(2, N) (N = 1, 2) is given.     

Superpotentials for Gauge and Conformal Supergravity Backgrounds

Effective superpotentials obtained by integrating out matter in super Yang-Mills and conformal supergravity backgrounds in SUSY theories are considered. The pure gauge and supergravity contributions (generalizing Veneziano-Yankielowicz terms) are derived by considering the case with matter fields in the fundamental representation of the gauge group. These contributions represent quantum corrections to the tree-level Yang-Mills and conformal supergravity actions. The classical equations of motion following from the conformal supergravity action require the background to be (super)conformally flat. This condition is unchanged by quantum corrections to the effective superpotential, irrespective of the matter content of the theory.     

Conformal invariance in N = 4 supersymmetric Yang-Mills theory

It is shown, by consideration of anomaly multiplets, that the maximally extended supersymmetric Yang-Mills theory is conformally invariant, assuming that the theory is supersymmetric and O(4)-invariant and that the structure of anomalies is given by the breakdown of conformal invariance in its coupling to supergravity.     

Classical Yang-Mills field equations coupled to a scalar triplet invariant under subgroups of the conformal group

Classical Yang-Mills-Scalar field equations on Minkowski space with gauge group SU (2) are determined. Solutions invariant up to a gauge transformation under a four-dimensional subgroup of the conformal group are determined for the case of a scalar matter triplet field.     

The supercurrent in five dimensions

The supercurrent multiplet is constructed for N=2 and 4 extended supersymmetries in five dimensions. The corresponding supergravity multiplets are also exhibited and have 40 + 40 and 128 + 128 components, respectively.     

Supersymmetric deformations of 3D SCFTs from tri-Sasakian truncation

We holographically study supersymmetric deformations of \(N=3\) and \(N=1\) superconformal field theories in three dimensions using four-dimensional \(N=4\) gauged supergravity coupled to three-vector multiplets with non-semisimple \(SO(3)\ltimes (\mathbf {T}^3,\hat{\mathbf {T}}^3)\) gauge group. This gauged supergravity can be obtained from a truncation of 11-dimensional supergravity on a tri-Sasakian manifold and admits both \(N=1,3\) supersymmetric and stable non-supersymmetric \(AdS_4\) critical points. We analyze the BPS equations for SO(3) singlet scalars in detail and study possible supersymmetric solutions. A number of RG flows to non-conformal field theories and half-supersymmetric domain walls are found, and many of them can be given analytically. Apart from these “flat” domain walls, we also consider \(AdS_3\)-sliced domain wall solutions describing two-dimensional conformal defects with \(N=(1,0)\) supersymmetry within the dual \(N=1\) field theory while this type of solutions does not exist in the \(N=3\) case.     

N = 4 Yang-Mills theory on the light cone

The 10-dimensional supersymmetric Yang-Mills theory is constructed in the light-cone gauge. When the theory is dimensionally reduced to four dimensions it is shown that the corresponding N = 4 theory is conveniently described in terms of a scalar superfield. This formalism avoids the problem of auxiliary fields but is Lorentz invariant only on the mass shell. Similar formalisms in terms of scalar superfields are also sketched for the other supersymmetric Yang-Mills as well as for N = 8 supergravity.     

Soft gauge algebras

Gauge transformations whose algebra closes only modulo field dependent terms (soft gauge algebras) are studied in detail. The results are explicitly applied to a supersymmetric gauge theory, to gravity and to conformal gravity, all seen as gauge theories overx-space; the obvious applications to supergravity are pointed out. A consistency requirement for the gauge transformations of those fields which appear in the algebra is seen to rule out “local translations” as independent gauge transformations.