Bound-state gravity from higher derivatives

In certain Lorentz-covariant higher-derivative field theories of spins < or =1, would-be ultraviolet divergences generate color-singlet poles as infrared divergences. Absence of higher-order poles implies ten-dimensional supersymmetric Yang-Mills with bound-state supergravity, in close analogy with open string theory.Comment: TeX file, 12 pages, 4 figure

Entropy-based convergence rates of greedy algorithms

We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the metric entropy of the solution manifold in Banach spaces. This contrasts with the classical analysis based on the Kolmogorov n-widths and enables us to obtain direct comparisons between the greedy algorithm error and the entropy numbers, where the multiplicative constants are explicit and simple. The entropy-based convergence estimate is sharp and improves upon the classical width-based analysis of reduced basis methods for elliptic model problems. In the second part, we derive a novel and simple convergence analysis of the classical orthogonal greedy algorithm for nonlinear dictionary approximation using the metric entropy of the symmetric convex hull of the dictionary. This also improves upon existing results by giving a direct comparison between the algorithm error and the metric entropy.Comment: 22 pages, no figure

Left-handed string and CHY amplitude at one loop

We propose a generalized left-handed (chiral) gauge choice for the genus one Riemann surface, realized through a singular gauge transformation of worldsheet coordinates. The transformation predominantly affects the logarithmic non-zero modes of the Green's function, leaving non-holomorphic and non-logarithmic modes unchanged. This procedure yields $\delta$-functions for chiral coordinates and box-diagram-like integrals in terms of modular parameters. The resulting $\delta$-functions formulate one-loop level Scattering Equations that simplify to satisfy the tree-level solutions, constraining the locations of the marked points. Subsequent integrals agree with the field-theoretic box diagram for the four-point amplitude, in accordance with the divergent $\epsilon$ expansions derived from dimensional regularization in the infrared limit. We conclude by highlighting potential avenues for future research, including the exploration of methodologies that preclude the need for worldsheet coordinates reparametrization and their implications for accurately capturing infrared behavior from modular parameter integrals

Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non zero mass is essential for this. This is reminiscent of Abelian Born-Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.Comment: Latex file, 40 pages.Some typos corrected and cosmetic change

Pion Transparency in 500 MeV C(pi,pi') Reactions?

The question whether there is a pion transparency in 500 MeV $C(\pi, \pi^{'})$ scatterings is studied using a semiclassical, hadronic transport model. The double differential cross sections of this reaction measured at LAMPF can be largely accounted for, if one uses energy-dependent, anisotropic angular distributions which are fitted to pion-nucleon scattering data for the decay of $\Delta(1232)$ and $N^*(1440)$ resonances. The remaining discrepancy between the data and the calculation sets a limit on effects of more exotic processes.Comment: Latex file, 11 pages, 3 figures availabe upon request. Phys. Lett. B in pres

Tool for Viewing Faults Under Terrain

Multi Surface Light Table (MSLT) is an interactive software tool that was developed in support of the QuakeSim project, which has created an earthquake- fault database and a set of earthquake- simulation software tools. MSLT visualizes the three-dimensional geometries of faults embedded below the terrain and animates time-varying simulations of stress and slip. The fault segments, represented as rectangular surfaces at dip angles, are organized into collections, that is, faults. An interface built into MSLT queries and retrieves fault definitions from the QuakeSim fault database. MSLT also reads time-varying output from one of the QuakeSim simulation tools, called "Virtual California." Stress intensity is represented by variations in color. Slips are represented by directional indicators on the fault segments. The magnitudes of the slips are represented by the duration of the directional indicators in time. The interactive controls in MSLT provide a virtual track-ball, pan and zoom, translucency adjustment, simulation playback, and simulation movie capture. In addition, geographical information on the fault segments and faults is displayed on text windows. Because of the extensive viewing controls, faults can be seen in relation to one another, and to the terrain. These relations can be realized in simulations. Correlated slips in parallel faults are visible in the playback of Virtual California simulations

Tamagawa Products for Elliptic Curves Over Number Fields

In recent work, Griffin, Ono, and Tsai constructs an $L-$series to prove that the proportion of short Weierstrass elliptic curves over $\mathbb{Q}$ with trivial Tamagawa product is $0.5054\dots$ and that the average Tamagawa product is $1.8183\dots$. Following their work, we generalize their $L-$series over arbitrary number fields $K$ to be $$L_{\mathrm{Tam}}(K; s):=\sum_{m=1}^{\infty}\frac{P_{\mathrm{Tam}}(K; m)}{m^s},$$ where $P_{\mathrm{Tam}}(K;m)$ is the proportion of short Weierstrass elliptic curves over $K$ with Tamagawa product $m$. We then construct Markov chains to compute the exact values of $P_{\mathrm{Tam}}(K;m)$ for all number fields $K$ and positive integers $m$. As a corollary, we also compute the average Tamagawa product $L_{\mathrm{Tam}}(K;-1)$. We then use these results to uniformly bound $P_{\mathrm{Tam}}(K;1)$ and $L_{\mathrm{Tam}}(K,-1)$ in terms of the degree of $K$. Finally, we show that there exist sequences of $K$ for which $P_{\mathrm{Tam}}(K;1)$ tends to $0$ and $L_{\mathrm{Tam}}(K;-1)$ to $\infty$, as well as sequences of $K$ for which $P_{\mathrm{Tam}}(K;1)$ and $L_{\mathrm{Tam}}(K;-1)$ tend to $1$.Comment: 40 pages, 9 figures, 17 table

Field Theoretic Study of Bilayer Membrane Fusion III: Membranes with Leaves of Different Composition

We extend previous work on homogeneous bilayers to calculate the barriers to fusion of planar bilayers which contain two different amphiphiles, a lamellae-former and a hexagonal former, with different compositions of the twoin each leaf. Self-consistent field theory is employed, and both standard and alternative pathways are explored. We first calculate these barriers as the amount of hexagonal former is increased equally in both leaves to levels appropriate to the plasma membrane of human red blood cells. We follow these barriers as the composition of hexagonal-formers is then increased in the cis layer and decreased in the trans layer, again to an extent comparable to the biological system. We find that, while the fusion pathway exhibits two barriers in both the standard and alternative pathways, in both cases the magnitudes of these barriers are comparable to one another, and small, on the order of 13 kT. As a consequence, one expects that once the bilayers are brought sufficiently close to one another to initiate the process, fusion should occur rapidly.Comment: 9 figure

Who changes the string coupling ?

In general bosonic closed string backgrounds the ghost-dilaton is not the only state in the semi-relative BRST cohomology that can change the dimensionless string coupling. This fact is used to establish complete dilaton theorems in closed string field theory. The ghost-dilaton, however, is the crucial state: for backgrounds where it becomes BRST trivial we prove that the string coupling becomes an unobservable parameter of the string action. For backgrounds where the matter CFT includes free uncompactified bosons we introduce a refined BRST problem by including the zero-modes "x" of the bosons as legal operators on the complex. We argue that string field theory can be defined on this enlarged complex and that its BRST cohomology captures accurately the notion of a string background. In this complex the ghost-dilaton appears to be the only BRST-physical state changing the string coupling.Comment: 34 pages, phyzz