Dual Superconformal Symmetry of N=2{\cal N}=2 Chern-Simons theory with Fundamental Matter at Large NN

Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like ${\cal N}=4$ SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level $2\to 2$ scattering amplitude in the 3d ${\cal N}=2$ Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the 't Hooft large $N$ limit, the $2\to 2$ scattering amplitude in this theory has been shown to be tree-level exact in non-anyonic channels, while having only an overall multiplicative coupling dependent renormalisation in the anyonic channel. Therefore, the dual superconformal symmetry that we demonstrate in this paper is all loop exact. This is unlike the previously studied highly supersymmetric theories where dual superconformal symmetry is anomalous at loop levels. Furthermore, we reverse the argument to study the extent to which dual superconformal invariance fixes the scattering amplitude in an ${\cal N}=2$ supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the $2\to2$ amplitude, while the coupling constant dependence remain unfixed. Further, we use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling dependence of scattering amplitude.Comment: V2 Published versio

Dual Superconformal Symmetry of \u3cem\u3eN\u3c/em\u3e = 2 Chern-Simons Theory with Fundamental Matter at Large \u3cem\u3eN\u3c/em\u3e

Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like N = 4 SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level 2 → 2 scattering amplitude in the 3d N = 2 Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the ’t Hooft large N limit, the 2 → 2 scattering amplitude in this theory has been shown to be tree-level exact in non-anyonic channels, while having only an overall multiplicative coupling dependent renormalisation in the anyonic channel. Therefore, the dual superconformal symmetry that we demonstrate in this paper is all loop exact. This is unlike the previously studied highly supersymmetric theories where dual superconformal symmetry is anomalous at loop levels. Furthermore, we reverse the argument to study the extent to which dual superconformal invariance fixes the scattering amplitude in an N = 2 supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the 2 → 2 amplitude, while the coupling constant dependence remain unfixed. Further, we use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling dependence of scattering amplitude

Method based on quasi variable mesh for solution of system of second order boundary value problems with mixed boundary conditions

A new numerical method with third order accuracy is presented for the solution of nonlinear two point boundary value problems(BVPs) with mixed boundary conditions using quasi variable mesh. In case of uniform mesh, method becomes fourth order. The method has been extended to vector form. Error analysis of the proposed scheme using a model problem is discussed. Application to fourth order nonlinear boundary value problem in coupled form is discussed. The proposed method is tested on two examples of linear and nonlinear BVPs and comparison with uniform mesh method has been made to prove the accuracy of the method.Publisher's Versio

Non-polynomial cubic spline discretization for system of non-linear singular boundary value problems using variable mesh

Abstract In this paper, we propose two generalized non-polynomial cubic spline schemes using a variable mesh to solve the system of non-linear singular two point boundary value problems. Theoretical analysis proves that the proposed methods have second- and third-order convergence. Both methods are applicable to singular boundary value problems. Numerical results are also provided to show the accuracy and efficiency of the proposed methods

Variable mesh discretization of system of nonlinear singular boundary value problems

In this paper two generalized numerical schemes using variable mesh has been developed to solve the system of nonlinear two point boundary value problems. Analytical convergence using a model fourth order problem has been provided. The order of convergence of the proposed methods are two and three. The methods are applicable to singular problems as well. Comparative study of numericals are given to prove the efficiency of the schemes.Publisher's Versio

Comparative study between open haemorrhoidectomy and transanal suture haemorrhoidopexy

Introduction:Haemorrhoids are the most common disorder of the anal canal. Different surgical modalities are available for the management of grade III and grade IV haemorrhoids which do not respond to the conservative managements. Post-operative pain and recurrence are the most common complications. Stapler haemorrhoidectomy, Doppler guided arterial ligation, laser though claim to be beneficial are costlier and not available in the rural areas, where open haemorrhoidectomy is the treatment of choice. In our study we have compared the open haemorrhoidectomy with trans anal suture haemorrhoidopexy which has all the benefits, can be accepted and performed for the rural people. Aim:To compare the outcome of open haemorrhoidectomy with trans anal suture haemorrhoidopexy in grade III and grade IV haemorrhoids. During the period Nov 2018-Oct 2020, 30 patients were operated by open haemorrhoidectomy and 30 by trans anal suture haemorrhoidopexy. Data for early and late complications along with period of hospital stay and time for return to work were collected and compared.Results:Suture haemorrhoidopexy resulted in less post-operative pain, less requirement of analgesia, less period of hospital stay, early return to work with less post-operative complications. It can be recommended as safe cost effective alternative procedure for haemorrhoidectomy