N = 8 supergravity

The complete structure of N = 8 supergravity is presented with an optional local SO(8) invariance. The SO(8) gauge interactions break E₇ invariance, but leave the local SU(8) unaffected. Exploiting E₇ × SU(8) invariance and using explicit lowest order results, we first derive the complete action and transformation laws. Subsequently, we introduce local SO(8) invariance and prove the consistency of the theory. Possible implications of our results are discussed.     

Geometry of coset spaces and massless modes of the squashed seven-sphere in supergravity

We derive some general results for Killing vectors on arbitrary coset manifolds and explicitly exhibit the squashed seven-sphere as the coset space Sp₄×Sp₂/Sp₂×Sp₂. Using these results, we then analyze the zero-mass sector of supergravity of the squashed S⁷ and argue that it is not interpretable as a spontaneously broken version of N=8 supergravity. We also point out the existence of a new solution which combines squashing and torsion.     

On the imaginary simple roots of the Borcherds algebra II9,1

In a recent paper [O. Bärwald, R.W. Gebert, M. Günaydin and H. Nicolai, preprint KCL-MTH-97-22, IASSNS-HEP-97/20, PSU-TH-178, AEI-029, hep-th/9703084, to appear in Commun. Math. Phys.] it was conjectured that the imaginary simple roots of the Borcherds algebra _II9,1 at level 1 are its only ones. We here propose an independent test of this conjecture, establishing its validity for all roots of norm − 8. However, the conjecture fails for roots of norm −10 and beyond, as we show by computing the simple multiplicities down to norm −24, which turn out to be remarkably small in comparison with the corresponding E₁₀ multiplicities. Our derivation is based on a modified denominator formula combining the denominator formulas for E₁₀ and _II9,1, and provides an efficient method for determining the imaginary simple roots. In addition, we compute the E₁₀ multiplicities of all roots up to height 231, including levels up to l = 6 and norms −42.     

Multiplet shortening in Osp(N,4)

We describe a new type of multiplet shortening in Osp(N,4) which resolves a long-standing puzzle in Kaluza-Klein supergravities. Multiplet shortening implies quantization of mass eigenvalues in units of the inverse AdS radius. While detailed proofs are presented only for N = 3, we discuss implications for N = 8 supergravity and derive the SO(8) assignments of all higher modes on the round seven-sphere.     

A transformation formula for integrals over superfields

We give an intrinsic definition of an integral over superfields and show that there is no Jacobi determinant in the transformation formula for such integrals.     

Gammaübergangswahrscheinlichkeit und Quasiteilchenapproximation

The transition probability of the isometricM4-transitions 1g _9/2-2p _1/2, 1h _11/2-2d _3/2 and 1i _13/2-2f _5/2 in near magic nuclei is calculated on the basis of the theory of finite Fermi systems. It is shown, that the constantg ₀ for the spin-spin interaction of quasiparticles, depends strongly on the special kind of representation for the single particle states. Using oscillator functions the valueg ₀=3.3 has to be taken, in order to get hindrance factors, which are approximately equal to one, whereas in the case of square well functions the constantg ₀=1.4 is necessary, in order to get agreement with the experimental transition probabilities.     

On the spectrum of Kaluza-Klein theories with non-compact internal spaces

We investigate the conditions under which Kaluza-Klein theories with non-compact internal spaces admit a discrete spectrum.     

Nontrivial solutions for Monge-Ampère type operators in convex domains

In this paper we prove existence and interior regularity of convex solutions of the Dirichlet problem for a class of Monge-Ampère type equations with right hand side vanishing on the boundary, by means of the fixed point index theory for Bakelman's weak solutions. The regularity in the interior follows from recent results of Caffarelli. Partially supported by M.U.R.S.T., Italy Partially supported by G.N.A.F.A. of C.N.R., Italy. This work was accomplished during a Humbold research stay at Karlsruhe and Heidelberg Universities.     

Elliptic equations for measures: Regularity and global bounds of densities

We consider elliptic equations of the form L^*μ=ν for measures on . The membership of solutions in the Sobolev classes is established under appropriate conditions on the coefficients of L. Bounds of the form (x)CΦ(x)⁻¹ for the corresponding densities are obtained.     

Electrophilically Activated Nitroalkanes in Synthesis of 3,4-Dihydroquinozalines

Nitroalkanes activated with polyphosphoric acid serve as efficient electrophiles in reactions with various nucleophilic amines. Strategically placed second functionality allows for the design of annulation reactions enabling preparation of various heterocycles. This strategy was employed to develop an innovative synthetic approach towards 3,4-dihydroquinazolines from readily available 2-(aminomethyl)anilines.