Almost product manifolds as the low energy geometry of Dirichlet branes

Any candidate theory of quantum gravity must address the breakdown of the classical smooth manifold picture of space-time at distances comparable to the Planck length. String theory, in contrast, is formulated on conventional space-time. However, we show that in the low energy limit, the dynamics of generally curved Dirichlet p-branes possess an extended local isometry group, which can be absorbed into the brane geometry as an almost product structure. The induced kinematics encode two invariant scales, namely a minimal length and a maximal speed, without breaking general covariance. Quantum gravity effects on D-branes at low energy are then seen to manifest themselves by the kinematical effects of a maximal acceleration. Experimental and theoretical implications of such new kinematics are easily derived. We comment on consequences for brane world phenomenology.Comment: 12 pages, invited article in European Physical Journal C, reprinted in Proceedings of the International School on Subnuclear Physics 2003 Erice (World Scientific

Labor Supply under Disability Insurance

There has been a significant recent growth in the Social Security Administration's Disability Insurance (DI) program, both in the number of covered workers under the program and in the amount of monthly benefits, One possible factor causing this growth has been labor supply disincentives under the pro- gram. The labor supply decision by an individual involves the effect of the disability benefit structure (potential benefits) on labor force participation. Probit estimates from the 1969 original sample of the Longitudinal Retirement History Study (LRHS) indicated an elasticity of participation with respect to benefits of -0031 for married men aged 58-63, and -.023 for all men of the same age group. The magnitude of these estimates are much less than those found by authors such as Parsons, and suggest relatively insignificant efficiency losses in terns of reduced work effort.

Labor Force Entry and Exit of Older Men: A Longitudinal Study

The labor force participation rate of older men under age 65 has shown a significant recent decline. Cross-sectional studies linking early retirement to increased Social Security income have also made explicit or implicit temporal projections of changes in participation in response to changes in benefits. However, use of cross-sectional estimates for projection purposes may run into several problems, including temporal dependence of the participation decision. This paper uses 2-year longitudinal data for men aged 58-62 in 1969 in order to trace changes in labor force behavior near retirement age. Results indicate significant effects of poor health, initial assets, and initial pension eligibility on the probabilities of exit and entry from the labor force. Social Security benefits are found to have insignificant or unexpected effects. The results also indicate evidence of temporal dependence of participation, suggesting caution in interpreting projections of cross-section estimates.

How quantizable matter gravitates: a practitioner's guide

We present the practical step-by-step procedure for constructing canonical gravitational dynamics and kinematics directly from any previously specified quantizable classical matter dynamics, and then illustrate the application of this recipe by way of two completely worked case studies. Following the same procedure, any phenomenological proposal for fundamental matter dynamics must be supplemented with a suitable gravity theory providing the coefficients and kinematical interpretation of the matter equations, before any of the two theories can be meaningfully compared to experimental data.Comment: 45 pages, no figure

A duality web of linear quivers

We show that applying the Bailey lemma to elliptic hypergeometric integrals on the $A_n$ root system leads to a large web of dualities for $\mathcal{N} = 1$ supersymmetric linear quiver theories. The superconformal index of Seiberg's SQCD with $SU(N_c)$ gauge group and $SU(N_f)\times SU(N_f)\times U(1)$ flavour symmetry is equal to that of $N_f-N_c-1$ distinct linear quivers. Seiberg duality further enlarges this web by adding new quivers. In particular, both interacting electric and magnetic theories with arbitrary $N_c$ and $N_f$ can be constructed by quivering an $s$-confining theory with $N_f=N_c+1$.Comment: v3: 10 pages, minor correction

Supersymmetric Casimir Energy and SL(3,Z)\mathrm{SL(3,\mathbb{Z})} Transformations

We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an $\mathrm{SL(3,\mathbb{Z})}$ transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for $\mathcal{N}=1$ SQCD and $\mathcal{N}=4$ supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally. We also use our method to derive an expression for the Casimir energy of the nonlagrangian $\mathcal{N}=2$ SCFT with $\mathrm{E_6}$ flavour symmetry. Furthermore, we predict an expression for Casimir energy of the $\mathcal{N}=1$ $\mathrm{SP(2N)}$ theory with $\mathrm{SU(8)\times U(1)}$ flavour symmetry that is part of a multiple duality network, and for the doubled $\mathcal{N}=1$ theory with enhanced $\mathrm{E}_7$ flavour symmetry.Comment: 20 pages, more explicit examples added, published in JHE

Geometry of physical dispersion relations

To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements to have predictive matter field dynamics and an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible.Comment: revised version, new section on applications added, 46 pages, 9 figure