Quantum Kaluza-Klein Compactification

Kaluza--Klein compactification in quantum field theory is analysed from the perturbation theory viewpoint. Renormalisation group analysis for compactification size dependence of the coupling constant is proposed.Comment: Latex2e, 10p

Complex Spinors and Unified Theories

In this paper delivered by Murray Gell-Mann at the Stony Brook Supergravity Workshop in 1979, several paths to unification are discussed, from N=8 supergravity to $SU_5$, $SO_{10}$, and $E_6$. Generalizations of $SO_{10}$ to spinor representations of larger groups are introduced. A natural mechanism for generating tiny neutrino masses is proposed in the context of $SO_{10}$, and finally, focus on $SU_3$ rather than $SU_2$ or $SO_3$ family symmetries is noted.Comment: Retro-preprint of 1979 paper. Originally published in Supergravity, P. van Nieuwenhuizen and D.Z. Freedman, eds, North Holland Publishing Co, 197

On Generalized Self-Duality Equations Towards Supersymmetric Quantum Field Theories Of Forms

We classify possible `self-duality' equations for p-form gauge fields in space-time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T invariant under a sub-group H of SO(D). Second, the representation for the SO(D) curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the `self-duality' equations can be candidates as gauge functions for SO(D)-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for dimensions greater than 9, for various p-form gauge fields.Comment: 20 pages, Late

Doubled resonances and unitarity

The constraints of unitarity on a multichannel partial-wave amplitude dominated by two nearby or coincident resonances are derived. The factorization conditions are discussed and used in the solution of these equations. The solutions permit variation in the relative heights of the two peaks in the cross section and variation in the depth of the dip. Single peaks appear in some cross sections, while doubled peaks appear in others. The single peak may be centered at the energy of the dip or displaced to either side, and the amplitude may be imaginary or real at the top of the single peak. The doubled-resonance amplitude is Reggeized and the narrow-width limit is investigated. The amplitude becomes a simple pole with an unfactorizable residue in this limit. Numerical examples of the solutions are also presented

K-K excitations on AdS_5 x S^5 as N=4 ``primary'' superfields

We show that the K-K spectrum of IIB string on AdS_5 x S_5 is described by ``twisted chiral'' N=4 superfields, naturally described in ``harmonic superspace'', obtained by taking suitable gauge singlets polynomials of the D3-brane boundary SU(n) superconformal field theory. To each p-order polynomial is associated a massive K-K short representation with 256 x 1/12 p^2(p^2 -1) states. The p=2 quadratic polynomial corresponds to the ``supercurrent multiplet'' describing the ``massless'' bulk graviton multiplet.Comment: 11 pages, LaTeX, no figure

On the Scalar Manifold of Exceptional Supergravity

We construct two parametrizations of the non compact exceptional Lie group G=E7(-25), based on a fibration which has the maximal compact subgroup K=(E6 x U(1))/Z_3 as a fiber. It is well known that G plays an important role in the N=2 d=4 magic exceptional supergravity, where it describes the U-duality of the theory and where the symmetric space M=G/K gives the vector multiplets' scalar manifold. First, by making use of the exponential map, we compute a realization of G/K, that is based on the E6 invariant d-tensor, and hence exhibits the maximal possible manifest [(E6 x U(1))/Z_3]-covariance. This provides a basis for the corresponding supergravity theory, which is the analogue of the Calabi-Vesentini coordinates. Then we study the Iwasawa decomposition. Its main feature is that it is SO(8)-covariant and therefore it highlights the role of triality. Along the way we analyze the relevant chain of maximal embeddings which leads to SO(8). It is worth noticing that being based on the properties of a "mixed" Freudenthal-Tits magic square, the whole procedure can be generalized to a broader class of groups of type E7.Comment: Talk given at the XVII European Workshop on String Theory, held at the University of Padua, September 5-9, 201

Supercurves

The TST-dual of the general 1/4-supersymmetric D2-brane supertube is identified as a 1/4-supersymmetric IIA `supercurve': a string with arbitrary transverse displacement travelling at the speed of light. A simple proof is given of the classical upper bound on the angular momentum, which is also recovered as the semi-classical limit of a quantum bound. The classical bound is saturated by a `superhelix', while the quantum bound is saturated by a bosonic oscillator state in a unique SO(8) representation.Comment: 1+14 pages, LaTe

Solving Gauge Invariant Systems without Gauge Fixing: the Physical Projector in 0+1 Dimensional Theories

The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require gauge fixing nor any additional degrees of freedom beyond the original ones---two characteristic features of all other available methods for quantising constrained dynamics---is put to work in the context of a general class of quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge groups are considered specifically, and a comprehensive understanding of the corresponding physical spectra is achieved in a straightforward manner, using only standard methods of coherent states and group theory which are directly amenable to generalisation to other Lie algebras. Results extend by far the few examples available in the literature from much more subtle and delicate analyses implying gauge fixing and the characterization of modular space.Comment: 32 pages, LaTeX fil

Notes on Equivalences and Higgs Branches in N=2 Supersymmetric Yang-Mills Theory

In this paper we investigate how various equivalences between effective field theories of $N=2$ SUSY Yang-Mills theory with matter can be understood through Higgs breaking, i.e. by giving expectation values to squarks. We give explicit expressions for the flat directions for a wide class of examples.Comment: 11 pages, Late

Uniqueness of the coordinate independent Spin(9)xSU(2) state of Matrix Theory

We explicitly prove, using some nontrivial identities involving gamma matrices, that there can be only one Spin(9)xSU(2) invariant state which depends only on fermionic variables