Setting the quantum integrand of M-theory

In anomaly-free quantum field theories the integrand in the bosonic functional integral--the exponential of the effective action after integrating out fermions--is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-theory the E(8)-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions. In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction of heterotic M-theory on cylinders.Comment: 52 pages; revised version for publication in Commun. Math. Phys. corrects a few typo

Quantization of anomaly coefficients in 6D N=(1,0)\mathcal{N}=(1,0) supergravity

We obtain new constraints on the anomaly coefficients of 6D $\mathcal{N}=(1,0)$ supergravity theories using local and global anomaly cancellation conditions. We show how these constraints can be strengthened if we assume that the theory is well-defined on any spin space-time with an arbitrary gauge bundle. We distinguish the constraints depending on the gauge algebra only from those depending on the global structure of the gauge group. Our main constraint states that the coefficients of the anomaly polynomial for the gauge group $G$ should be an element of $2 H^4(BG;\mathbb{Z}) \otimes \Lambda_S$ where $\Lambda_S$ is the unimodular string charge lattice. We show that the constraints in their strongest form are realized in F-theory compactifications. In the process, we identify the cocharacter lattice, which determines the global structure of the gauge group, within the homology lattice of the compactification manifold.Comment: 42 pages. v3: Some clarifications, typos correcte

Low-speed longitudinal and lateral-directional aerodynamic characteristics of the X-31 configuration

An experimental investigation of a 19 pct. scale model of the X-31 configuration was completed in the Langley 14 x 22 Foot Subsonic Tunnel. This study was performed to determine the static low speed aerodynamic characteristics of the basic configuration over a large range of angle of attack and sideslip and to study the effects of strakes, leading-edge extensions (wing-body strakes), nose booms, speed-brake deployment, and inlet configurations. The ultimate purpose was to optimize the configuration for high angle of attack and maneuvering-flight conditions. The model was tested at angles of attack from -5 to 67 deg and at sideslip angles from -16 to 16 deg for speeds up to 190 knots (dynamic pressure of 120 psf)

Resource Utilization Prediction: A Proposal for Information Technology Research

Research into predicting long-term resource needs has been faced with a very difficult problem of extending the accuracy period beyond the immediate future. Business forecasting has overcome this limitation by successfully incorporating the concept of human interaction as the basis of prediction patterns at the hourly, daily, weekly, monthly, and yearly time frames. Computer resource utilization is also impacted by human interaction therefore influencing research into predictability of resource usage based on human access patterns. Emulated human web server access data was captured in a feasibility study that used time series analysis to predict future resource usage. For prediction beyond several minutes, results indicate that the majority of projected resource usage was within an 80% confidence level thus supporting the foundation of future resource prediction work in this area

The Uncertainty of Fluxes

In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes modulo torsion can be simultaneously measured. We also develop the Hamilton theory of self-dual fields, noting that they are quantized by Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is Z/2-graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the Ramond-Ramond field in string theory, showing that its K-theory class cannot be measured.Comment: 33 pages; minor modifications for publication in Commun. Math. Phy

Revolutionaries and spies: Spy-good and spy-bad graphs

We study a game on a graph $G$ played by $r$ {\it revolutionaries} and $s$ {\it spies}. Initially, revolutionaries and then spies occupy vertices. In each subsequent round, each revolutionary may move to a neighboring vertex or not move, and then each spy has the same option. The revolutionaries win if $m$ of them meet at some vertex having no spy (at the end of a round); the spies win if they can avoid this forever. Let $\sigma(G,m,r)$ denote the minimum number of spies needed to win. To avoid degenerate cases, assume |V(G)|\ge r-m+1\ge\floor{r/m}\ge 1. The easy bounds are then \floor{r/m}\le \sigma(G,m,r)\le r-m+1. We prove that the lower bound is sharp when $G$ has a rooted spanning tree $T$ such that every edge of $G$ not in $T$ joins two vertices having the same parent in $T$. As a consequence, \sigma(G,m,r)\le\gamma(G)\floor{r/m}, where $\gamma(G)$ is the domination number; this bound is nearly sharp when $\gamma(G)\le m$. For the random graph with constant edge-probability $p$, we obtain constants $c$ and $c'$ (depending on $m$ and $p$) such that $\sigma(G,m,r)$ is near the trivial upper bound when $r<c\ln n$ and at most $c'$ times the trivial lower bound when $r>c'\ln n$. For the hypercube $Q_d$ with $d\ge r$, we have $\sigma(G,m,r)=r-m+1$ when $m=2$, and for $m\ge 3$ at least $r-39m$ spies are needed. For complete $k$-partite graphs with partite sets of size at least $2r$, the leading term in $\sigma(G,m,r)$ is approximately $\frac{k}{k-1}\frac{r}{m}$ when $k\ge m$. For $k=2$, we have \sigma(G,2,r)=\bigl\lceil{\frac{\floor{7r/2}-3}5}\bigr\rceil and \sigma(G,3,r)=\floor{r/2}, and in general $\frac{3r}{2m}-3\le \sigma(G,m,r)\le\frac{(1+1/\sqrt3)r}{m}$.Comment: 34 pages, 2 figures. The most important changes in this revision are improvements of the results on hypercubes and random graphs. The proof of the previous hypercube result has been deleted, but the statement remains because it is stronger for m<52. In the random graph section we added a spy-strategy resul