Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

TL;DR

The paper tackles the problem of understanding how central charges evolve along RG flows between UV and IR fixed points in four-dimensional supersymmetric gauge theories. It develops two nonperturbative techniques to compute flows of primary central functions $b$, $c$, and $a$ in SU($N_c$) theories within the conformal window and shows $a_{UV}-a_{IR}>0$, providing evidence for an a-theorem analogue and RG irreversibility. It finds that flavor central charges can flow upward (no universal $b$-theorem) while the Euler anomaly coefficient $a$ decreases along flows, and presents detailed results for electric and magnetic SQCD, including exact IR values and consistency with duality. It also derives gravitational central-function flows, with mixed behavior for $c$ and robust evidence for monotonic decrease of $a$. The work advances nonperturbative understanding of conformal dynamics in SUSY gauge theories and informs the broader search for irreversibility in four-dimensional QFT.

Abstract

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.