Gauge internal symmetry in extended supergravity

Extended supergravity theories with global O(2) and SO(3) internal symmetry have recently been constructed, and a mechanism which implements local O(2) and SO(3) gauge invariance is given here. The introduction of a minimal gauge coupling automatically leads to a $\text{spin}\text{-}\text{3}\text{2}$ mass and a cosmological term in order to preserve local supersymmetry. Local internal symmetry for a $\text{spin}\text{-}\text{3}\text{2}$ field is related to spontaneous breakdown of global supersymmetry. Perturbation theory results which confirm the physical consistency of the system are given.     

1616 supergravity coupled to matter: The low energy limit of the superstring

We analyze irreducible, N = 1 supergravity theories with 16 fermionic degrees of freedom. The lagrangians for pure $\text{16}\text{16}$ supergravity, and for $\text{16}\text{16}$ supergravity coupled to arbitrary chiral superfields are constructed. These theories are shown to have natural SU(1,1) non-compact symmetry. The low energy field theory limit of the superstring is conjectured to be of this type.     

Extended supergravity on the supergroup manifold: N = 3 and N = 2 theories

In this paper I construct the group-manifold first-order formulation of N = 2 and N = 3 supergravity based on the $\text{Osp}\text{(}\text{4}\text{2}\text{)}\text{and Osp}\text{(}\text{4}\text{3}\text{)}$ supergroups, respectively. In the case N = 2, a group manifold version of the theory was already presented in a previous paper. Here a simpler formulation is given which shows exact factorization in the SO(2) subgroup absent in the previous one. Particular attention is paid to the algebraic role played by the $\text{spin}\text{-}\text{1}\text{2}$ field which is the novel feature of the N = 3 case with respect to N = 2. It is shown how the “non-geometrical” term in the gravitino transformation law in the N = 2 theory arises from the rheonomic symmetry mechanism.     

Consistency in explicitly broken N = 1 supergravity with matter couplings

Using N = 1 supergravity coupled to general, gauged, N = 1 matter, we show that the addition of a wide class of explicit supersymmetry breaking terms in the N = 1 matter fields can still lead to the spin $\text{3}\text{2}$ field satisfying an equation of motion in which propagation is causal. We argue that a similar result holds in the case of N = 2 supergravity coupled to matter, plus explicit terms.     

Anomalies in supergravity

There has been much interest recently in the problem of anomalies in field theory. This is a consequence of recent work on the regularization of stress tensors, and of renewed interest in the axial vector anomaly. In this paper, I shall present a derivation of both the trace anomaly and the axial vector anomaly for the spin-$\text{3}\text{2}$ Majorana field using a zeta function regularization procedure. This result is also of interest in supergravity and extended supergravity.     

Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups $\text{SP}\text{(2n,}\text{R}$ and $\text{SO}\text{(2n)}{}^1$ from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n?4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)¹ and E₇(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E₇₍₇₎ and SO(12)¹ obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)¹.     

Symmetries of coset spaces and Kaluza-Klein supergravity

Known theorems about the isometry group of a general coset space $\text{G}\text{H}$ are reviewed. The Killing vectors on $\text{G}\text{H}$ are explicitly constructed. Rescalings of the coset vielbeins are discussed, and a simple criterion to find which rescalings preserve the isometry group is given. A general expression for the Riemann and Ricci tensors in terms of the rescaled vielbeins and the group structure constants is derived. These results have useful applications in Kaluza-Klein theories. As an example, the round and the squashed seven-spheres that have been used to compactify d = 11 supergravity are discussed, and it is shown that they can be identified with two appropriately rescaled coset spaces $\text{SO(5)}\text{SO(3)}$.     

Chiral fermion generations from higher-dimensional gravity

We discuss a six-dimensional SO(12) gauge theory which can be obtained from pure gravity in 18 dimensions coupled to a Majorana-Weyl spinor, if the ground state is characterized by a noncompact internal space without boundary with small finite volume. The six-dimensional SO(12) theory spontaneously compactifies to a four-dimensional SO(10) theory with local generation group SU(2)_G × U(1)_G. We obtain an even number of chiral fermion generations transforming as ($\text{16, k, ±}\text{1}\text{2}$) under SO(10) × SU(2)_G × U(1)_G. Adding a scalar field to the six-dimensional theory provides us with fields carrying all the quantum numbers needed for a realistic spontaneous symmetry breakdown to SU(3)_c × U(1)_e.m.     

On the new definition of off-shell effective action

We analyze the recently proposed definition of the off-shell, gauge-invariant, gauge-independent, effective action $\text{Γ}$, utilizing an invariant metric on the field space. It is shown how to establish correspondence between $\text{Γ}$ and the standard effective action, calculated in some particular (Landau-type) gauge. Several examples are explicitly discussed, including Yang-Mills theory, the effective potential in scalar QED, and one-loop quantum gravity. Generalization to the case of super-invariant theories (e.g. super-Yang-Mills and supergravity) is also presented.     

Approaches to the gravitational spin-32 axial anomaly

The $\text{spin}\text{-}\text{3}\text{2}$ axial anomaly is discussed from various points of view. Two consistent theories for a $\text{spin}\text{-}\text{3}\text{2}$ field interacting with gravity are considered: supergravity and a real quantized $\text{spin}\text{-}\text{3}\text{2}$ field in a classical gravitational background. The Feynman graph method, the zeta function regularization method, the point splitting method and the topological method all yield the same result for the latter theory, in agreement with that first found by Christensen and Duff.     

The axial and trace anomalies for spin 32

The axial and trace anomalies for a real spin $\text{3}\text{2}$ field interacting with a background gravitational field, as in simple supergravity, is computed. The axial anomaly result differs from that of Van Nieuwenhuizen and Vermaseren.     

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Non-gauge spin-32 fields from supercovariantly constant spinors

We point out a limiting procedure which enables one to construct in supergravity theories non-gauge, linearized spin-$\text{3}\text{2}$ fields with the aid of the supercovariantly constant spinors. We give an explicit application of the procedure for N = 2 supergravity.     

Massive vector multiplets in supergravity

Starting from a vector multiplet we construct general lagrangians using the tensor calculus. After a Weyl rescaling and other field redefinitions we find lagrangians for the massive spin $\text{(1,}\text{1}\text{2}\text{,}\text{1}\text{2}\text{, 0)}$ model coupled to supergravity. Among the class of lagrangians which we consider we find no supersymmetry breaking.     

Chirality,self-duality,and supergravity counterterms

The restrictions imposed by chirality invariance on higher-loop counterterms in supergravity are obtained. It is shown that their dependence on gravitational curvature and on spin-$\text{3}\text{2}$ field strength is such that they vanish when these quantities are self-or anti-self-dual. Implications regarding quantum corrections in the instanton sector are discussed.     

Spectrum (super-) symmetries of particles in a Coulomb potential

The Schrödinger equation for a spin-0 particle in the field of a dyon is obtained by dimensional reduction of the four-dimensional harmonic oscillator; the reduction is effected by imposing an equivariance condition on the wave functions of the latter system. This geometrical construction allows for a simple derivation of the SO(4, 2) spectrum symmetry of the dyon system. A supermultiplet of one $\text{spin}\text{-}\text{1}\text{2}$ and two spin-0 particles in a Coulomb potential is demonstrated to possess an N = 2 conformal supersymmetry through a generalization of the same method. The states and wave functions for these systems can be obtained from the representation theory of the corresponding symmetry algebras. A particular case for which this approach provides a complete group theoretical analysis is that of the Pauli equation for a $\text{spin}\text{-}\text{1}\text{2}$ particle in the field of a dyon.     

The supergroup manifold formulation of the Wess-Zumino multiplet revisited: The supercurrent and the supergravity auxiliary fields

In this paper we provide a consistent first-order group-manifold formulation of the Wess-Zumino system. It is shownhow the well-known auxiliary fields of the ($\text{1}\text{2}$, 0, 0) system arise by supplementing Bianchi identities with the “second-order constraints”; that is, those equations allowing the transition from the first order to the second order of the theory. When the ($\text{1}\text{2}$, 0, 0) multiplet is coupled to N = 1 supergravity and the torsion “second-order constraint” is implemented, we get a non-minimal set of auxiliary fields (scalar, pseudoscalar axial vector and a spinor). We argue this to be the fundamental set of auxiliary fields. The so-called “minimal set” is not coordinate invariant and can be recovered only by adding a non-geometrical constraint.     

An example of the no-hair conjecture in supergravity

We provide support to the “no-hair” conjecture in supergravity by showing that the Schwarzschild background cannot sustain any “true” static helicity-$\text{3}\text{2}$ perturbation which falls off faster than $\text{1}\text{r}$ because it is not possible to satisfy regularity conditions at the horizon.