Poles in the SS-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.Comment: 12 pages, minor correction

The large D black hole dynamics in AdS/dS backgrounds

We have constructed a class of perturbative dynamical black hole solutions in presence of cosmological constant. We have done our calculation in large number of dimensions. The inverse power of dimension has been used as the perturbation parameter and our calculation is valid upto the first subleading order. The solutions are in one to one correspondence with a dynamical membrane and a velocity field embedded in the asymptotic geometry. Our method is manifestly covariant with respect to the asymptotic geometry. One single calculation and the same universal result works for both dS and AdS geometry or in case of AdS for both global AdS and Poincare patch. We have checked our final answer with various known exact solutions and the known spectrum of Quasi Normal modes in AdS/dS.Comment: 74 pages. v2: Minor changes, typos correcte

Unstable ‘black branes’ from scaled membranes at large D

It has recently been demonstrated that the dynamics of black holes at large $D$ can be recast as a set of non gravitational membrane equations. These membrane equations admit a simple static solution with shape $S^{D-p-2} \times R^{p,1}$. In this note we study the equations for small fluctuations about this solution in a limit in which amplitude and length scale of the fluctuations are simultaneously scaled to zero as $D$ is taken to infinity. We demonstrate that the resultant nonlinear equations, which capture the Gregory- Laflamme instability and its end point, exactly agree with the effective dynamical `black brane' equations of Emparan Suzuki and Tanabe. Our results thus identify the `black brane' equations as a special limit of the membrane equations and so unify these approaches to large $D$ black hole dynamics.Comment: 10 pages, references adde

Automatic detection of malignant melanoma using boundary gradient information in dermoscopy images

This thesis demonstrates an algorithm which uses local border features, primarily derived from the border gradient, to help determine whether the lesion is a malignant melanoma or a benign lesion. Although this algorithm uses manually-marked lesion borders, it could be included in a fully automatic routine. A Prewitt algorithm with a window size proportional to the area of the lesion is used to calculate the gradient over the entire lesion boundary. This gradient value is used to calculate various boundary features, such as mean, standard deviation, and direction of maximum gradient. The dark and white areas inside the lesion combined with the gradient measurements are used to generate additional features. All these features are used as inputs to a neural network to classify the lesion as malignant or benign. A total of 90 different features were fed to the neural network. The features that gave the most accurate separation were a combination of dark area features and white area features. These features when combined with some other features like the boundary length gave a diagnostic accuracy of 80.5% for the test set of 48 malignant and 198 benign images --Abstract, page iii

Large D membrane for higher derivative gravity and black hole second law

We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in 1/D upto linear order in the Gauss-Bonnet (GB) parameter β. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in 1/D but non-perturbatively in β for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes

Black holes in presence of cosmological constant: second order in 1 D 1D \frac{1}{D}

Abstract We have extended the results of [1] upto second subleading order in an expansion around large dimension D. Unlike the previous case, there are non-trivial metric corrections at this order. Due to our ‘background-covariant’ formalism, the dependence on Ricci and the Riemann curvature tensor of the background is manifest here. The gravity system is dual to a dynamical membrane coupled with a velocity field. The dual membrane is embedded in some smooth background geometry that also satisfies the Einstein equation in presence of cosmological constant. We explicitly computed the corrections to the equation governing the membrane-dynamics. Our results match with earlier derivations in appropriate limits. We calculated the spectrum of QNM from our membrane equations and matched them against similar results derived from gravity

Regularized phase-space volume for the three-body problem

The micro-canonical phase-space volume for the three-body problem is an elementary quantity of intrinsic interest, and within the flux-based statistical theory, it sets the scale of the disintegration time. While the bare phase-volume diverges, we show that a regularized version can be defined by subtracting a reference phase-volume, which is associated with hierarchical configurations. The reference quantity, also known as a counter-term, can be chosen from a 1-parameter class. The regularized phase-volume of a given (negative) total energy, $\bar\sigma(E)$, is evaluated. First, it is reduced to a function of the masses only, which is sensitive to the choice of a regularization scheme only through an additive constant. Then, analytic integration is used to reduce the integration to a sphere, known as shape sphere. Finally, the remaining integral is evaluated numerically, and presented by a contour plot in parameter space. Regularized phase-volumes are presented for both the planar three-body system and the full 3d system. In the test mass limit, the regularized phase-volume is found to become negative, thereby signalling the breakdown of the non-hierarchical statistical theory. This work opens the road to the evaluation of $\bar\sigma(E,L)$, where $L$ is the total angular momentum, and it turn, to comparison with simulation determined disintegration times.Comment: 27 pages, 6 figure