The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points

Charging the Superconformal Index

The superconformal index is an important invariant of superconformal field theories. In this note we refine the superconformal index by inserting the charge conjugation operator C. We construct a matrix integral for this charged index for N = 4 SYM with SU(N) gauge group. The key ingredient for the construction is a “charged character,” which reduces to Tr(C) for singlet representations of the ...

The existence of fixed points for the ·/GI/1 queue

A celebrated theorem of Burke’s asserts that the Poisson process is a fixed point for a stable exponential single server queue; that is, when the arrival process is Poisson, the equilibrium departure process is Poisson of the same rate. This paper considers the following question: Do fixed points exist for queues which dispense i.i.d. services of finite mean, but otherwise of arbitrary distribu...

Index for Non-relativistic Superconformal Field Theories

We study the highest-weight representation ofN = 2 supersymmetric Schrödinger algebra which appears in non-relativistic superconformal field theories in (1+2) dimension. We define the index for the non-relativistic superconformal field theories and study its properties. As a concrete example, we compute the index for the nonrelativistic limit of N = 6 superconformal Chern-Simons-matter theory r...

New iteration process for approximating fixed points in Banach spaces

‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our res...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points