Strong gauging or decoupling ghost matter

TL;DR

This paper explores the effects of strong gauging on conformal field theories, highlighting cases where the central charge increases and discussing the limitations of dilaton effective theory due to non-unitarity.

Contribution

It introduces the concept of strong gauging via decoupling ghost matter and analyzes its impact on the central charge in conformal field theories, challenging existing theoretical arguments.

Findings

Strong gauging can increase the central charge in certain RG flows.

Dilaton effective field theory does not apply straightforwardly to strong gauging.

Non-unitarity from ghost matter prevents definitive positivity results.

Abstract

Gauging extra matter is a common way to couple two CFTs discontinuously. We may consider gauging matter by strongly coupled gauge theories at criticality rather than by weakly coupled (asymptotic free) gauge theories. It often triggers relevant deformations and possibly leads to a non-trivial fixed point. In many examples such as the IR limit of SQCDs (and their variants), the relevant RG flow induced by this strong gauging makes the total central charge $a$ increase rather than decrease compared with the sum of the original decoupled CFTs. The dilaton effective field theory argument given by Komargodski and Schwimmer does not apply because strong gauging is not a simple deformation by operators in the original two decoupled CFTs and it may not be UV complete. When the added matter is vector-like, one may emulate strong gauging in a UV completed manner by decoupling of ghost matter. While the UV completed description makes the dilaton effective field theory argument possible, due to the non-unitarity, we cannot conclude the positivity of the central charge difference in accordance with the observations in various examples that show the contrary.