Adjoint Trapping: A New Phenomenon at Strong 't Hooft Coupling

TL;DR

This paper investigates a novel phenomenon called adjoint trapping in strongly coupled N=4 supersymmetric Yang-Mills theory, revealing how adjoint matter becomes localized in small regions and identifying a transition point where bound states become unbound.

Contribution

The study introduces the concept of adjoint trapping at strong coupling and analyzes the transition from bound to unbound states using Wilson loop methods, extending understanding of quarkonium behavior.

Findings

Adjoint matter is surprisingly light and small at large 't Hooft coupling.

A sharp transition occurs at J ≈ 0.22√λ where states become unbound.

In confining theories, the transition becomes a rapid crossover with changing state size.

Abstract

Adding matter of mass m, in the fundamental representation of SU(N), to N=4 supersymmetric Yang-Mills theory, we study ``generalized quarkonium'' containing a (s)quark, an anti(s)quark, and J massless (or very light) adjoint particles. At large 't Hooft coupling $\lambda$ >> 1, the states of spin <= 1 are surprisingly light (Kruczenski et al., hep-th/0304032) and small (hep-th/0312071) with a J-independent size of order $\sqrt{\lambda}/m$. This ``trapping'' of adjoint matter in a region small compared with its Compton wavelength and compared to any confinement scale in the theory is an unfamiliar phenomenon, as it does not occur at small $\lambda$. We explore adjoint trapping further by considering the limit of large J. In particular, for J >> $\sqrt{\lambda}$ >> 1, we expect the trapping phenomenon to become unstable. Using Wilson loop methods, we show that a sharp transition, in which the generalized quarkonium states become unbound (for massless adjoints) occurs at $J \simeq 0.22 \sqrt{\lambda}$. If the adjoint scalars of N=4 are massive and the theory is confining (as, for instance, in N=1* theories) then the transition becomes a cross-over, across which the size of the states changes rapidly from ~$\sqrt{\lambda}/m$ to something of order the confinement scale ~ $\Lambda^{-1}$.