Effective Action of Matter Fields in Four-Dimensional String Orientifolds

We study various aspects of the Kahler metric for matter fields in N=1,2 orientifold compactifications of type IIB string theory. The result has an infrared-divergent part which reproduces the field- theoretical anomalous dimensions, and a moduli-dependent part which comes from N=2 sectors of the orientifold. For the N=2 orientifolds, we also compute the disk amplitude for two matter fields on the boundary and a twisted closed string modulus in the bulk. Our results are in agreement with supersymmetry: the singlet under the SU(2)_R R-symmetry has vanishing coupling, while the coupling of the SU(2)_R triplet does not vanish.Comment: 24 pages, JHEP LaTex, no figures, v2: references added, typos correcte

Heat content with singular initial temperature and singular specific heat

Let (M,g) be a compact Riemannian manifold without boundary. Let D be a compact subdomain of M with smooth boundary. We examine the heat content asymptotics for the heat flow from D into M where both the initial temperature and the specific heat are permitted to have controlled singularities on the boundary of D. The operator driving the heat process is assumed to be an operator of Laplace typ

Expected volume of intersection of Wiener sausages and heat kernel norms on compact Riemannian manifolds with boundary

Estimates are obtained for the expected volume of intersection of independent Wiener sausages in Euclidean space in the small time limit. The asymptotic behaviour of the weighted diagonal heat kernel norm on compact Riemannian manifolds with smooth boundary is obtained in the small time limi

String Loop Corrections to Kahler Potentials in Orientifolds

We determine one-loop string corrections to Kahler potentials in type IIB orientifold compactifications with either N=1 or N=2 supersymmetry, including D-brane moduli, by evaluating string scattering amplitudes.Comment: 80 pages, 4 figure

The strength of countable saturation

We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.Comment: Corrected typos in Lemma 3.4 and the final paragraph of the conclusio

An efficient, multiple range random walk algorithm to calculate the density of states

We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant density of states is modified continuously to produce locally flat histograms. This method permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions. It should also be useful for the study of complex systems with a rough energy landscape.Comment: 4 pages including 4 ps fig

Fine-Grained Complexity Analysis of Two Classic TSP Variants

We analyze two classic variants of the Traveling Salesman Problem using the toolkit of fine-grained complexity. Our first set of results is motivated by the Bitonic TSP problem: given a set of $n$ points in the plane, compute a shortest tour consisting of two monotone chains. It is a classic dynamic-programming exercise to solve this problem in $O(n^2)$ time. While the near-quadratic dependency of similar dynamic programs for Longest Common Subsequence and Discrete Frechet Distance has recently been proven to be essentially optimal under the Strong Exponential Time Hypothesis, we show that bitonic tours can be found in subquadratic time. More precisely, we present an algorithm that solves bitonic TSP in $O(n \log^2 n)$ time and its bottleneck version in $O(n \log^3 n)$ time. Our second set of results concerns the popular $k$-OPT heuristic for TSP in the graph setting. More precisely, we study the $k$-OPT decision problem, which asks whether a given tour can be improved by a $k$-OPT move that replaces $k$ edges in the tour by $k$ new edges. A simple algorithm solves $k$-OPT in $O(n^k)$ time for fixed $k$. For 2-OPT, this is easily seen to be optimal. For $k=3$ we prove that an algorithm with a runtime of the form $\tilde{O}(n^{3-\epsilon})$ exists if and only if All-Pairs Shortest Paths in weighted digraphs has such an algorithm. The results for $k=2,3$ may suggest that the actual time complexity of $k$-OPT is $\Theta(n^k)$. We show that this is not the case, by presenting an algorithm that finds the best $k$-move in $O(n^{\lfloor 2k/3 \rfloor + 1})$ time for fixed $k \geq 3$. This implies that 4-OPT can be solved in $O(n^3)$ time, matching the best-known algorithm for 3-OPT. Finally, we show how to beat the quadratic barrier for $k=2$ in two important settings, namely for points in the plane and when we want to solve 2-OPT repeatedly.Comment: Extended abstract appears in the Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016