A Note on Effective String Theory

Motivated by the possibility of an effective string description for the infrared limit of pure Yang-Mills theory, we present a toy model for an effective theory of random surfaces propagating in a target space of $D>2$. We show that the scaling exponents for the fixed area partition function of the theory are apparently well behaved. We make some observations regarding the usefulness of this toy model.Comment: 17 pages, LATEX, UTTG-21-9

On Relativistic Brane Probes in Singular Spacetimes

We study the relativistic dynamics of brane probes in singular warped spacetimes and establish limits for such analysis. The behavior of the semiclassical brane probe wave functions implies that unitarity boundary conditions can be imposed at the singularity.Comment: 9 pages, 1 figure, typos corrected and references adde

Exponential Hierarchy From Spacetime Variable String Vacua

It is shown that non-supersymmetric spacetime varying string vacua can lead to an exponential hierarchy between the electroweak and the gravitational scales. The hierarchy is naturally generated by a string coupling of O(1).Comment: 22 pages, Latex, 2 figure

Eigenvalue Density, Li’s Positivity, and the Critical Strip

We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution; this subsequently allows us to formally derive an integral expression for the Li coefficients associated with the Riemann xi-function which, in particular, indicate that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and also offer a physical interpretation of the result and discuss the Hilbert-Polya approach