Gauge Theory Correlators from Non-Critical String Theory

We suggest a means of obtaining certain Green's functions in 3+1-dimensional ${\cal N} = 4$ supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. The non-critical string theory is related to critical string theory in anti-deSitter background. We introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory. Correlation functions of operators in the gauge theory are related to the dependence of the supergravity action on the boundary conditions. From the quadratic terms in supergravity we read off the anomalous dimensions. For operators that couple to massless string states it has been established through absorption calculations that the anomalous dimensions vanish, and we rederive this result. The operators that couple to massive string states at level $n$ acquire anomalous dimensions that grow as 2\left (n g_{YM} \sqrt {2 N} )^{1/2} for large `t Hooft coupling. This is a new prediction about the strong coupling behavior of large $N$ SYM theory.Comment: 15 pages, harvmac with btxmac; minor revisions, 1 reference added, the version to appear in Physics Letters

Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach

The subset sum problem (SSP) can be briefly stated as: given a target integer $E$ and a set $A$ containing $n$ positive integer $a_j$, find a subset of $A$ summing to $E$. The \textit{density} $d$ of an SSP instance is defined by the ratio of $n$ to $m$, where $m$ is the logarithm of the largest integer within $A$. Based on the structural and statistical properties of subset sums, we present an improved enumeration scheme for SSP, and implement it as a complete and exact algorithm (EnumPlus). The algorithm always equivalently reduces an instance to be low-density, and then solve it by enumeration. Through this approach, we show the possibility to design a sole algorithm that can efficiently solve arbitrary density instance in a uniform way. Furthermore, our algorithm has considerable performance advantage over previous algorithms. Firstly, it extends the density scope, in which SSP can be solved in expected polynomial time. Specifically, It solves SSP in expected $O(n\log{n})$ time when density $d \geq c\cdot \sqrt{n}/\log{n}$, while the previously best density scope is $d \geq c\cdot n/(\log{n})^{2}$. In addition, the overall expected time and space requirement in the average case are proven to be $O(n^5\log n)$ and $O(n^5)$ respectively. Secondly, in the worst case, it slightly improves the previously best time complexity of exact algorithms for SSP. Specifically, the worst-case time complexity of our algorithm is proved to be $O((n-6)2^{n/2}+n)$, while the previously best result is $O(n2^{n/2})$.Comment: 11 pages, 1 figur

Universal interpretation of efficacy parameter in perturbed nonequilibrium systems

The fluctuation theorems have remained one of the cornerstones in the study of systems that are driven far out of equilibrium, and they provide strong constraints on the fraction of trajectories that behave atypically in light of the second law. They have mainly been derived for a predetermined external drive applied to the system. However, to improve the efficiency of a process, one needs to incorporate protocols that are modified by receiving feedbacks about the recent state of the system, during its evolution. In such a case, the forms of the conventional fluctuation theorems get modified, the correction term involving terms that depend on the way the reverse/conjugate process is defined, namely, the rules of using feedback in order to generate the exact time-reversed/conjugate protocols. We show in this paper that this can be done in a large number of ways, and in each case we would get a different expression for the correction terms. This would in turn lead to several lower bounds on the mean work that must be performed on the system, or on the entropy changes. Here we analyze a form of the extended fluctuation theorems that involves the efficacy parameter, and find that this form gives rise to a lower bound for the mean work that retains a consistent physical meaning regardless of the design of feedback along the conjugate process, as opposed to the case of the previously mentioned form of the modified fluctuation theorems.Comment: 7 pages, 1 figur

Hierarchical Gaussian process mixtures for regression

As a result of their good performance in practice and their desirable analytical properties, Gaussian process regression models are becoming increasingly of interest in statistics, engineering and other fields. However, two major problems arise when the model is applied to a large data-set with repeated measurements. One stems from the systematic heterogeneity among the different replications, and the other is the requirement to invert a covariance matrix which is involved in the implementation of the model. The dimension of this matrix equals the sample size of the training data-set. In this paper, a Gaussian process mixture model for regression is proposed for dealing with the above two problems, and a hybrid Markov chain Monte Carlo (MCMC) algorithm is used for its implementation. Application to a real data-set is reported

Nuttier Bubbles

We construct new explicit solutions of general relativity from double analytic continuations of Taub-NUT spacetimes. This generalizes previous studies of 4-dimensional nutty bubbles. One 5-dimensional locally asymptotically AdS solution in particular has a special conformal boundary structure of $AdS_3\times S^1$. We compute its boundary stress tensor and relate it to the properties of the dual field theory. Interestingly enough, we also find consistent 6-dimensional bubble solutions that have only one timelike direction. The existence of such spacetimes with non-trivial topology is closely related to the existence of the Taub-NUT(-AdS) solutions with more than one NUT charge. Finally, we begin an investigation of generating new solutions from Taub-NUT spacetimes and nuttier bubbles. Using the so-called Hopf duality, we provide new explicit time-dependent backgrounds in six dimensions.Comment: 32 pages, 1 figure; v.3. typos corrected. Matches the published versio

Positive pion absorption on 3He using modern trinucleon wave functions

We study pion absorption on 3He employing trinucleon wave functions calculated from modern realistic NN interactions (Paris, CD Bonn). Even though the use of the new wave functions leads to a significant improvement over older calculations with regard to both cross section and polarization data, there are hints that polarization data with quasifree kinematics cannot be described by just two-nucleon absorption mechanisms.Comment: 14 pages, 6 figure

Supergravity Description of the Large N Noncommutative Dipole Field Theories

We consider system of Dp-branes in the presence of a nonzero B field with one leg along brane worldvolume and the other transverse to it. We study the corresponding supergravity solutions and show that the worldvolume theories decouple from gravity for $p\leq 5$. Therefore these solutions provide dual description of large N noncommutative dipole field theories. We shall only consider those systems which preserve 8 supercharges in the branes worldvolume. We analyze the system of M5-branes and NS5-branes in the presence of nonzero C field and RR field with one leg along the transverse direction and the others along the worldvolume of the brane, respectively. This could provide a new deformation of (2,0) and little string field theories. Finally, we study the Wilson loops using the dual gravity descriptions.Comment: 24 pages, Latex fil

Particle Production in Matrix Cosmology

We consider cosmological particle production in 1+1 dimensional string theory. The process is described most efficiently in terms of anomalies, but we also discuss the explicit mode expansions. In matrix cosmology the usual vacuum ambiguity of quantum fields in time-dependent backgrounds is resolved by the underlying matrix model. This leads to a finite energy density for the "in" state which cancels the effect of anomalous particle production.Comment: 24 pages, 1 figure; v2: references added, minor change

How to Stop (Worrying and Love) the Bubble: Boundary Changing Solutions

We discover that a class of bubbles of nothing are embedded as time dependent scaling limits of previous spacelike-brane solutions. With the right initial conditions, a near-bubble solution can relax its expansion and open the compact circle. Thermodynamics of the new class of solutions is discussed and the relationships between brane/flux transitions, tachyon condensation and imaginary D-branes are outlined. Finally, a related class of simultaneous connected S-branes are also examined.Comment: 47 pages; v2 introduction to Weyl cards added, comments added, references added, typos corrected, matches JHEP versio

Twisted sectors in three-dimensional gravity

Twisted sectors --solutions to the equations of motion with non-trivial monodromies-- of three dimensional Euclidean gravity are studied. We argue that upon quantization this new sector of the theory provides the necessary (and no more) degrees of freedom to account for the Bekenstein-Hawking entropy.Comment: An unnecessary restriction removed. To appear in PRD. Revtex, no figures, 20 p