Deserfest

PREFACE.

CONTENTS.

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Causality is as important a principle in biology as it is in physics. Through a mechanism that modifies the strengths of connections between neurons on the basis of the temporal ordering of the signals they conduct, neurons can identify which of their thousands of inputs are causally related to their responses. By modeling this phenomenon and calculating its impact, we have generated predictions about the effects of experience on the activity of neurons in the hippocampal area of the rat brain that have been verified experimentally. The enhancement of causal inputs through this mechanism has significant implications for learning from experience.

We consider string phenomenological models based on 11D Horava-Witten M-theory with 5-branes in the bulk. If the 5-branes cluster close to the distant orbifold plane (d_n ≡ 1 - z_n ≃ 0.1) and if the topological charges of the physical plane vanish , then the Witten ∊ terms (to first order) are correctly small and a qualitative picture of the quark and lepton mass hierarchy arises without significant fine tuning. If right handed neutrinos exist, a possible gravitationally induced cubic holomorphic contribution to the Kahler potential can exist scaled by the 11D Planck mass. These terms give rise to Dirac neutrino masses at the electroweak scale. This mechanism (different from the see-saw mechanism) is seen to account for both the atmospheric and solar neutrino oscillations. The model also gives rise to possible non-universal soft breaking A parameters in the u and d second and third generation quark sector which naturally can account for the possible (2.4σ) break down of the Standard Model predictions in the recent B-factory data for the B → ϕK_s decays.

No abstract received.

I describe the light-cone gauge formulation of supersymmetric theories. In particular I show the great resemblance of 10-dimensional super Yang-Mills theory and 11-dimensional supergravity.

The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically simplified by the use of the Arnowitt-Deser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solution is describable, at each (generic) spatial point, as a billiard motion in an auxiliary Lorentzian space. For certain Einstein-matter systems, notably for pure Einstein gravity in any spacetime dimension D and for the particular Einstein-matter systems arising in String theory, the billiard tables describing asymptotic cosmological behaviour are found to be identical to the Weyl chambers of some Lorentzian Kac-Moody algebras. In the case of the bosonic sector of supergravity in 11 dimensional spacetime the underlying Lorentzian algebra is that of the hyperbolic Kac-Moody group E₁₀, and there exists some evidence of a correspondence between the general solution of the Einstein-three-form system and a null geodesic in the infinite dimensional coset space E₁₀/K(E₁₀), where K(E₁₀) is the maximal compact subgroup of E₁₀.

In M-theory vacua with vanishing 4-form F₍₄₎, one can invoke ordinary Riemannian holonomy H ⊂ Spin (10,1) to account for unbroken supersymmetries n = 1, 2, 3, 4, 6, 8, 16, 32. However, in the presence of non-zero F₍₄₎, Riemannian holonomy must be extended to generalized holonomy to account for more exotic fractions of supersymmetry. The resulting number of M-theory vacuum supersymmetries, 0 ≤ n ≤ 32, is then given by the number of singlets appearing in the decomposition of the 32 of SL(32, ℝ) under .

We report on the gauged supergravity analysis of Type IIB vacua on K3 × T²/ℤ₂ orientifold in the presence of D3 - D7–branes and fluxes. We discuss supersymmetric critical points correspond to Minkowski vacua and the related fixing of moduli, finding agreement with previous analysis. An important role is played by the choice of the symplectic holomorphic sections of special geometry which enter the computation of the scalar potential. The related period matrix is explicitly given. The relation between the special geometry and the Born–Infeld action for the brane moduli is elucidated.

I review some recent work on consistent reductions of gravity and supergravity theories. An important distinction is made between reductions on a group manifold ('De-Witt reductions') for which reduction is unproblematic, and reductions on a coset space ('Pauli reductions'), which are in general inconsistent. It is emphasised that only special conspiracies between the gravity and matter sectors allow consistent Pauli reductions. In some cases, one may obtain a Pauli reduction by taking a Kaluza style U(1) quotient of a De-Witt reduction. Of special interest are models derived from string theory. That based on the bosonic string allows consistent reduction on S³ ≡ SO(4)/SO(3) in all dimensions. A truly remarkable example of a consistent reduction is the six-dimensional supergravity model of Salam and Sezgin. This allows a supersymmetric monopole reduction on S² to give a supersymmetric coupling of gravity, SU(2) Yang-Mills and an axion and a dilaton in four dimensions with a flat supersymmetric Minkowski vacuum. Subject to the assumption of maximal spacetime symmetry, the ground state is unique. The model may be obtained by a consistent reduction from ten-dimensional supergravity on the non-compact riemannian hyperboloid followed by a Kaluza reduction and chiral truncation.

We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two "superpotentials".

Higher-order invariants and their rôle as possible counterterms for supergravity theories in four dimensions are reviewed. The construction of R⁴ superinvariants in string theory and M-theory in D = 10 and D = 11 is discussed.

When 4-dimensional general relativity is extended by a 3-dimensional gravitational Chern-Simons term an apparent violation of diffeomorphism invariance is extinguished by the dynamical equations of motion for the modified theory. The physical predictions of this recently proposed model show little evidence of symmetry breaking, but require the vanishing of the gravitation Pontryagin density.

We review the status of "Einstein-Æther theory", a generally covariant theory of gravity coupled to a dynamical, unit timelike vector field that breaks local Lorentz symmetry. Aspects of waves, stars, black holes, and cosmology are discussed, together with theoretical and observational constraints. Open questions are stressed.

This preliminary report proposes integrating the Maxwell equations in Minkowski spacetime using coordinates where the spacelike surfaces are hyperboloids asymptotic to null cones at spatial infinity. The space coordinates are chosen so that Scri+ occurs at a finite coordinate and a smooth extension beyond Scri+ is obtained. The question addressed is whether a Cauchy evolution numerical integration program can be easily modified to compute this evolution. In the spirit of the von Neumann and Richtmyer artificial viscosity which thickens a shock by many orders of magnitude to facilitate numerical simulation, I propose artificial cosmology to thicken null infinity Scri+ to approximate it by a de Sitter cosmological horizon where, in conformally compactified presentation, it provides a shell of purely outgoing null cones where asymptotic waves can be read off as data on a spacelike pure outflow outer boundary. This should be simpler than finding Scri+ as an isolated null boundary or imposing outgoing wave conditions at a timelike boundary at finite radius.

The ADM Formalism is discussed in the context of 2 + 1-dimensional gravity, uniting two areas of relativity theory in which Stanley Deser has been particularly active. For spacetimes with topology ℝ×T² the partially reduced and fully reduced ADM formalism are related and quantized, and the role of "large diffeomorphisms" (the modular group) in the quantum theory is illustrated.

After a brief review of integrability, first in the absence and then in the presence of a boundary, I outline the construction of actions for the N = 1 and N = 2 boundary sine-Gordon models. The key point is to introduce Fermionic boundary degrees of freedom in the boundary actions.

We review the recent construction of a three-dimensional effective field theory that describes the interactions of the infinitely many N = 8 supermultiplets contained in the spin-1 Kaluza-Klein towers that arise in the compactification of six-dimensional N = (2,0) supergravity on AdS₃ × S³. The theory forms a gauged N = 8 super-gravity with gauge group SO(4) ⋉ T_∞ over the infinite dimensional coset space SO(8, ∞)/(SO(8) × SO(∞)), where T_∞ is an infinite dimensional translation subgroup of SO(8, ∞).

I review some interesting features of massive gravity in two maximally symmetric backgrounds: Anti de Sitter space and Minkowski space. While massive gravity in AdS can be seen as a spontaneously broken, UV safe theory, no such interpretation exists yet in the flat-space case. Here, I point out the problems encountered in trying to find such completion, and possible mechanisms to overcome them.

The Seiberg–Witten solution plays a central role in the study of supersymmetric gauge theories. As such, it provides a proving ground for a wide variety of techniques to treat such problems. In this review we concentrate on the role of IIA string theory/M theory and the Dijkgraaf–Vafa matrix model, though integrable models and microscopic instanton calculations are also of considerable importance in this subject.

We investigate the perturbative dynamics of noncommutative topologically massive gauge theories with softly broken supersymmetry. The deformed dispersion relations induced by noncommutativity are derived and their implications on the quantum consistency of the theory are discussed.

No abstract received.

The divergence structure of supergravity has long been a topic of concern because of the theory's non-renormalizability. In the context of string theory, where perturbative finiteness should be achieved, the supergravity counterterm structures remain nonetheless of importance because they still occur, albeit with finite coefficients. The leading nonvanishing supergravity counterterms have a particularly rich structure that has a bearing on the preservation of supersymmetry in string vacua in the presence of perturbative string corrections. Although the holonomy of such manifolds is deformed by the corrections, a Killing spinor structure nevertheless can persist. The integrability conditions for the existence of such Killing spinors remarkably remain consistent with the perturbed effective field equations.

Three dimensional quantum gravity with torus universe, T² × ℝ, topology is reformulated as the motion of a relativistic point particle moving in an Sl(2, ℤ) orbifold of flat Minkowski spacetime. The latter is precisely the three dimensional Milne Universe studied recently by Russo as a background for Strings. We comment briefly on the dynamics and quantization of the model.

Attraction between quarks is a fundamental aspect of QCD. It is plausible that several of the most profound aspects of low-energy QCD dynamics are connected to diquark correlations, including: paucity of exotics (which is the foundation of the quark model and of traditional nuclear physics), similarity of mesons and baryons, color superconductivity at high density, hyperfine splittings, ΔI = 1/2 rule, and some striking features of structure and fragmentation functions. After a brief overview of these issues, I discuss how diquarks can be studied in isolation, both phenomenologically and numerically, and present approximate mass differences for diquarks with different quantum numbers. The mass-loaded generalization of the Chew-Frautschi formula provides an essential tool.

I argue against the widespread notion that manifest de Sitter invariance on the full de Sitter manifold is either useful or even attainable in gauge theories. Green's functions and propagators computed in a de Sitter invariant gauge are generally more complicated than in some noninvariant gauges. What is worse, solving the gauge-fixed field equations in a de Sitter invariant gauge generally leads to violations of the original, gauge invariant field equations. The most interesting free quantum field theories possess no normalizable, de Sitter invariant states. This precludes the existence of de Sitter invariant propagators. Even had such propagators existed, infrared divergent processes would still break de Sitter invariance.

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