A limitation of Markov representation for stationary processes

AbstractThe existence of a representation of a stationary process as an instantaneous function of a real, irreducible Markov chain (Harris chain) imposes important restrictions on the distribution of the process. We construct a countably-valued stationary process with a very strong mixing property for which such a representation does not exist

Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordstr\"{o}m black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case $M^2> Q^2$. This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Swcharzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit $Q \rightarrow 0$. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.Comment: To be appeared in International Journal of Theoretical Physic

The (p,q) String Tension in a Warped Deformed Conifold

We find the tension spectrum of the bound states of p fundamental strings and q D-strings at the bottom of a warped deformed conifold. We show that it can be obtained from a D3-brane wrapping a 2-cycle that is stabilized by both electric and magnetic fluxes. Because the F-strings are Z_M-charged with non-zero binding energy, binding can take place even if (p,q) are not coprime. Implications for cosmic strings are briefly discussed.Comment: 17 pages, 1 figur

New Jacobi-Like Identities for Z_k Parafermion Characters

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.Comment: 72 pages (or 78/2 = 39 pages in reduced format

Adding a Brane to the Brane-Anti-Brane Action in BSFT

We attempt to generalize the effective action for the D-brane-anti-D-brane system obtained from boundary superstring field theory (BSFT) by adding an extra D-brane to it to obtain a covariantized action for 2 D-branes and 1 anti-D-brane. We discuss the approximations made to obtain the effective action in closed form. Among other properties, this effective action admits solitonic solutions of codimension 2 (vortices) when one of the D-brane is far separated from the brane-anti-brane pair.Comment: 23 pages, 2 figures, minor revision

Generally Covariant Actions for Multiple D-branes

We develop a formalism that allows us to write actions for multiple D-branes with manifest general covariance. While the matrix coordinates of the D-branes have a complicated transformation law under coordinate transformations, we find that these may be promoted to (redundant) matrix fields on the transverse space with a simple covariant transformation law. Using these fields, we define a covariant distribution function (a matrix generalization of the delta function which describes the location of a single brane). The final actions take the form of an integral over the curved space of a scalar single-trace action built from the covariant matrix fields, tensors involving the metric, and the covariant distribution function. For diagonal matrices, the integral localizes to the positions of the individual branes, giving N copies of the single-brane action.Comment: 34 pages, LaTeX. v2: comments and refs adde

Localized modes at a D-brane--O-plane intersection and heterotic Alice strings

We study a system of $N_c$ $D3$-branes intersecting $D7$-branes and $O7$-planes in 1+1-dimensions. We use anomaly cancellation and string dualities to argue that there must be chiral fermion zero-modes on the $D3$-branes which are localized near the $O7$-planes. Away from the orientifold limit we verify this by using index theory as well as explicit construction of the zero-modes. This system is related to F-theory on K3 and heterotic matrix string theory, and the heterotic strings are related to Alice string defects in $\mathcal{N}=4$ Super-Yang-Mills. In the limit of large $N_c$ we find an $AdS_3$ dual of the heterotic matrix string CFT.Comment: 44 pages, typos corrected, version published in JHE

Kac and New Determinants for Fractional Superconformal Algebras

We derive the Kac and new determinant formulae for an arbitrary (integer) level $K$ fractional superconformal algebra using the BRST cohomology techniques developed in conformal field theory. In particular, we reproduce the Kac determinants for the Virasoro ($K=1$) and superconformal ($K=2$) algebras. For $K\geq3$ there always exist modules where the Kac determinant factorizes into a product of more fundamental new determinants. Using our results for general $K$, we sketch the non-unitarity proof for the $SU(2)$ minimal series; as expected, the only unitary models are those already known from the coset construction. We apply the Kac determinant formulae for the spin-4/3 parafermion current algebra ({\em i.e.}, the $K=4$ fractional superconformal algebra) to the recently constructed three-dimensional flat Minkowski space-time representation of the spin-4/3 fractional superstring. We prove the no-ghost theorem for the space-time bosonic sector of this theory; that is, its physical spectrum is free of negative-norm states.Comment: 33 pages, Revtex 3.0, Cornell preprint CLNS 93/124

Charge, geometry, and effective mass in the Kerr-Newman solution to the Einstein field equations

It has been shown that for the Reissner-Nordstrom solution to the vacuum Einstein field equations charge, like mass, has a unique space-time signature [Found. Phys. 38, 293-300 (2008)]. The presence of charge results in a negative curvature. This work, which includes a discussion of effective mass, is extended here to the Kerr-Newman solution.Comment: To appear in Foundations of Physics. Misprints have been corrected. 14 pages, 4 figure

Beyond equilibrium: Re-evaluating physical modelling of fluvial systems to represent climate changes

© 2018 Elsevier B.V. The interactions between water, sediment and biology in fluvial systems are complex and driven by multiple forcing mechanisms across a range of spatial and temporal scales. In a changing climate, some meteorological drivers are expected to become more extreme with, for example, more prolonged droughts or more frequent flooding. Such environmental changes will potentially have significant consequences for the human populations and ecosystems that are dependent on riverscapes, but our understanding of fluvial system response to external drivers remains incomplete. As a consequence, many of the predictions of the effects of climate change have a large uncertainty that hampers effective management of fluvial environments. Amongst the array of methodological approaches available to scientists and engineers charged with improving that understanding, is physical modelling. Here, we review the role of physical modelling for understanding both biotic and abiotic processes and their interactions in fluvial systems. The approaches currently employed for scaling and representing fluvial processes in physical models are explored, from 1:1 experiments that reproduce processes at real-time or time scales of 10 −1 -10 0 years, to analogue models that compress spatial scales to simulate processes over time scales exceeding 10 2 –10 3 years. An important gap in existing capabilities identified in this study is the representation of fluvial systems over time scales relevant for managing the immediate impacts of global climatic change; 10 1 – 10 2 years, the representation of variable forcing (e.g. storms), and the representation of biological processes. Research to fill this knowledge gap is proposed, including examples of how the time scale of study in directly scaled models could be extended and the time scale of landscape models could be compressed in the future, through the use of lightweight sediments, and innovative approaches for representing vegetation and biostabilisation in fluvial environments at condensed time scales, such as small-scale vegetation, plastic plants and polymers. It is argued that by improving physical modelling capabilities and coupling physical and numerical models, it should be possible to improve understanding of the complex interactions and processes induced by variable forcing within fluvial systems over a broader range of time scales. This will enable policymakers and environmental managers to help reduce and mitigate the risks associated with the impacts of climate change in rivers