E.G. Floratos

A note on the classical symmetries of the closed bosonic membranes

Abstract We determine the infinite-dimensional Lie algebras of the classical symmetries for the closed bosonic membranes. In the case of the torus membrane, T 2 =S 1 ×S 1 , we find a particular Virasoro subalgebra of these symmetries and we discuss possible implications for the spectrum of the quantum torus membrane.

Octonionic gravitational instantons

Abstract We construct eight-dimensional gravitational instantons by solving appropriate self-duality equations for the spin-connection. The particular gravitational instanton we present has Spin (7) holonomy and, in a sense, it is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a removable bolt singularity which is topologically S 4 and its boundary at infinity is the squashed S 7 . We also lift our solutions to ten and eleven dimensions and construct fundamental string and membrane configurations that preserve 1/16 of the original supersymmetries.

New realizations of the Virasoro algebra as membrane symmetries

Abstract We construct new realizations of the Virasoro algebra as subalgebras of area preserving diffeomorphisms of surfaces, which are the membrane symmetries. For the membrane torus, the SDiff(T 2 ) algebra has a central extension of unique form and the corresponding Virasoro subalgebras are in general realized as non-trivial central extensions. These central extensions should be relevant to the question whether quantum string excitations may be contained in the membrane spectrum.

A two-loop calculation of the mass gap for the O(N) model in finite volume☆

Abstract The mass gap for the quantum O(N) non-linear sigma model in a finite volume in two dimensions is calculated to two-loop order in perturbation theory. This result is used to estimate the mass gap of the infinite-volume O(3) model to be about 2.1 Λ MS ± 10% . The calculation is carried out using dimensional regularization with both compact and non-compact extra dimensions, with the same result in both cases.

Tree-level scattering amplitudes in de Sitter space diverge

Abstract We derive the growing large-distance behaviour of the graviton propagator in de Sitter space to any order in perturbation. By explicit computation we show that tree-level scattering amplitudes diverge as a consequence of the logarithmic increase of the transverse and traceless part of the graviton propagator.

Finite temperature closed bosonic string in a finite volume

Abstract Paying attention to the modular invariance and using a covariant canonical gauge (the proper time gauge), we calculate the free energy of a noninteracting gas of closed bosonic strings in a 25-dimensional torus of finite size. The result differs in form from the modular non-invariant result of Polchinski, but can be shown to be equal to it.

Coherent states in Finite Quantum Mechanics

Abstract The “harmonic oscillator”, introduced by Itzykson and Balian, is considered, on finite phase-space lattices with the structure of Galois fields GF [ p 2 ]. We study this system at the classical and quantum mechanical level. Explicit construction of the quantum eigenstates provides us with a detailed understanding of the spectrum of scales relevant to this model. We construct also the coherent states appropriate to the finite Heisenberg-Weyl and affine groups. Possible applications are discussed.

Large top and bottom Yukawa couplings in minimal supersymmetry

Abstract We present analytic expressions for the top and bottom Yukawa couplings in the context of the minimal supersymmetric standard model when both couplings h t , o , h b , o are large at the unification scale. For sufficiently large h t , o , h b , o , using as input the central value of the bottom mass m b ( m b )=4.25 GeV, we find that the top mass lies in the range m t ≈(174–178) GeV, while tan β ≈ (55–58). Implications on the evolution of the scalar masses and the radiative symmetry breaking scenario are discussed.

A note on the supersymmetries of the self-dual supermembrane

Abstract In this letter we discuss the supersymmetry issue of the self-dual supermembranes in (8+1) and (4+1)-dimensions. We find that all genuine solutions of the (8+1)-dimensional supermembrane, based on the exceptional group G 2 , preserve one of the sixteen supersymmetries while all solutions in (4+1)-dimensions preserve eight of them.

The mass gap of the 2d CPn−1 model in finite volume

Abstract The mass gap of the 2d CP n −1 model in finite volume is calculated up to two-loop order in pertubation theory. An estimate for the infinite-volume mass gap is given.