Multiplet Recombination and the CFT Distance Conjecture

TL;DR

This paper explores infinite-distance limits in 4D ${ m extbf{N}=2}$ superconformal field theories, revealing a novel protected BPS tower arising from multiplet recombination, with implications for the CFT Distance Conjecture and AdS duals.

Contribution

It introduces a new protected BPS tower in ${ m extbf{N}=2}$ SCFTs, arising from multiplet recombination, and verifies this through explicit one-loop computations.

Findings

Identification of a protected BPS tower with exponential degeneracy.

Verification of the structure via explicit one-loop calculations.

Connection between multiplet recombination and the CFT Distance Conjecture.

Abstract

Motivated by quantum gravity and the CFT Distance Conjecture, we study infinite-distance limits in four-dimensional ${\cal N}=2$ superconformal field theories with higher-dimensional conformal manifolds and their AdS duals. We focus on partial decoupling limits where a gauge sector becomes weakly coupled while an interacting sector persists. We analyse the structure of towers of states emerging in these limits. The weakly coupled sector contributes, among others, the massless higher-spin tower predicted by the CFT Distance Conjecture exhibiting polynomial degeneracy. The key novelty is the appearance of a protected BPS tower in the interacting sector, characterised by exponential degeneracy and masses at the AdS scale. This structure follows from multiplet recombination in the ${\cal N}=2$ superconformal algebra: As unprotected long multiplets hit the unitarity bound at weak coupling, they recombine into protected short multiplets. We verify this picture through an explicit one-loop computation in the simplest two-node quiver gauge theory with a two-dimensional conformal manifold.