Daniel Z. Freedman

Gauge Internal Symmetry in Extended Supergravity

Abstract 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 spin - 3 2 mass and a cosmological term in order to preserve local supersymmetry. Local internal symmetry for a spin - 3 2 field is related to spontaneous breakdown of global supersymmetry. Perturbation theory results which confirm the physical consistency of the system are given.

Ricci Flat Kahler Manifolds and Supersymmetry

Abstract A class of supersymmetric non-linear σ-models obtained previously is shown to generate a set of explicit Ricci-flat Kahler metrics of even complex dimension. The two-dimensional case is a self-dual gravitational instanton, very probably the Eguchi-Hansen metric, while higher dimensional cases may coincide with manifolds of Calabi.

Pure de Sitter supergravity

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local N = 1 supersymmetry. The supergravity multiplet interacts with a nilpotent Goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and Goldstino, no scalars. In the global limit when the supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where the Goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

Stability of AdS(p) x M(q) compactifications without supersymmetry

We study the stability of Freund-Rubin compactifications, AdS_p x M_q, of p+q-dimensional gravity theories with a q-form field strength and no cosmological term. We show that the general AdS_p x S^q vacuum is classically stable against small fluctuations, in the sense that all modes satisfy the Breitenlohner-Freedman bound. In particular, the compactifications used in the recent discussion of the proposed bosonic M-theory are perturbatively stable. Our analysis treats all modes arising from the graviton and the q-form, and is completely independent of supersymmetry. From the masses of the linearized perturbations, we obtain the dimensions of some operators in possible holographic dual CFTs. Solutions with more general compact Einstein spaces need not be stable, and in particular AdS_p x S^n x S^{q-n} is unstable for q = 9. We also study the AdS_4 x S^6 compactification of massive type IIA supergravity, which differs from the usual Freund-Rubin compactification in that there is a cosmological term already in ten dimensions. This nonsupersymmetric vacuum is unstable.

Gauge quantization for spin-32 fields☆

Abstract The free massless Rarita-Schwinger equation and a recently constructed interacting field theory known as supergravity are invariant under fermionic gauge transformations. Gauge field quantization techniques are applied in both cases. For the free field the Faddeev-Popov ansatz for the generating functional is justified by showing that it is equivalent to canonical quantization in a particular gauge. Propagators are obtained in several gauges and are shown to be ghost-free and causal. For supergravity the Faddeev-Popov ansatz is presented and the gauge fixing and determinant terms are discussed in detail in a Lorentz covariant gauge. The Slavnov-Taylor identity is obtained. It is argued that supergravity theory is free from the difficulty of acausal wave propagation of the type found by Velo and Zwanziger and that pole residues in tree approximation S-matrix elements are positive as required by unitarity.

N=1 supersymmetric product group theories in the Coulomb phase

We study the low-energy behavior of N=1 supersymmetric gauge theories with product gauge groups SU(N){sup M} and M chiral superfields transforming in the fundamental representation of two of the SU(N) factors. These theories are in the Coulomb phase with an unbroken U(1){sup N{minus}1} gauge group. For N{ge}3, M{ge}3 the theories are chiral. The low-energy gauge-kinetic functions can be obtained from hyperelliptic curves which we derive by considering various limits of the theories. We present several consistency checks of the curves including confinement through the addition of mass perturbations and other limits. {copyright} {ital 1997} {ital The American Physical Society}

Stability of AdS_p x M_q Compactifications Without Supersymmetry

We study the stability of Freund-Rubin compactifications, AdS_p x M_q, of p+q-dimensional gravity theories with a q-form field strength and no cosmological term. We show that the general AdS_p x S^q vacuum is classically stable against small fluctuations, in the sense that all modes satisfy the Breitenlohner-Freedman bound. In particular, the compactifications used in the recent discussion of the proposed bosonic M-theory are perturbatively stable. Our analysis treats all modes arising from the graviton and the q-form, and is completely independent of supersymmetry. From the masses of the linearized perturbations, we obtain the dimensions of some operators in possible holographic dual CFTs. Solutions with more general compact Einstein spaces need not be stable, and in particular AdS_p x S^n x S^{q-n} is unstable for q = 9. We also study the AdS_4 x S^6 compactification of massive type IIA supergravity, which differs from the usual Freund-Rubin compactification in that there is a cosmological term already in ten dimensions. This nonsupersymmetric vacuum is unstable.

Supergravity Field Theories and the Art of Constructing Them

During the past year Lagrangian field theories in four dimensional space-time have been developed which have a new gauge principle, namely, local supersymmetry. The gauge field of supersymmetry transformation is the spin 3/2 Rarita-Schwinger field and it necessarily occurs in these theories together with the vierbein field which describes gravitation. A variety of constructions of supergravity field theories have now been given which include vector, spinor, and scalar fields. Although none of them seems to apply directly to experiment, I take the attitude that they are all interesting because they are the basic constructions associated with a gauge principle of considerable mathematical elegance. In qualitative terms, what has been achieved is an extension of general relativity in which gravitation is closely linked with the fundamental concept of anti-commuting fermion fields. Unification of lower spin fields with the graviton occurs in some models, and supergravity practitioners hope that a corresponding unification of gravitation with other particle interactions can be achieved. Since there are as yet no signals from experiment that nature is aware of our efforts, we look for theoretical signals. The improved renormalizability situation in supergravity, which will be discussed by Peter van Nieuwenhuizen at this conference, may be one such signal.

Stability ofAdSp×Mqcompactifications without supersymmetry

We study the stability of Freund-Rubin compactifications, AdS_p x M_q, of p+q-dimensional gravity theories with a q-form field strength and no cosmological term. We show that the general AdS_p x S^q vacuum is classically stable against small fluctuations, in the sense that all modes satisfy the Breitenlohner-Freedman bound. In particular, the compactifications used in the recent discussion of the proposed bosonic M-theory are perturbatively stable. Our analysis treats all modes arising from the graviton and the q-form, and is completely independent of supersymmetry. From the masses of the linearized perturbations, we obtain the dimensions of some operators in possible holographic dual CFTs. Solutions with more general compact Einstein spaces need not be stable, and in particular AdS_p x S^n x S^{q-n} is unstable for q = 9. We also study the AdS_4 x S^6 compactification of massive type IIA supergravity, which differs from the usual Freund-Rubin compactification in that there is a cosmological term already in ten dimensions. This nonsupersymmetric vacuum is unstable.

Response to "Boundary conditions and renormalization in anti-de Sitter supersymmetry"

It is agreed that the boundary conditions at spatial infinity do not affect the renormalization of the Wess-Zumino model in anti--de Sitter space.