Size instabilities in rings of chaotic synchronized systems

We consider the behavior of rings of unidirectionally coupled chaotic systems. When the number of oscillators in the ring is below a certain critical number the behavior of the ring is chaotic synchronized, while above this threshold an instability appears. The novel feature is that this instability may yield a chaotic rotating wave if some conditions are fulfilled

Exact Bremsstrahlung functions in ABJM theory

In this paper we study the Bremsstrahlung functions for the 1/6 BPS and the 1/2 BPS Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric ($B^{\varphi}_{1/6}$) and R-symmetry ($B^{\theta}_{1/6}$) deformations of the 1/6 BPS Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for $B^{\theta}_{1/6}$ based on a known result for $B^{\varphi}_{1/6}$. Subsequently, we explore the consequences of this relation for the 1/2 BPS Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function $h(\lambda)$. During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.Comment: 43 pages, 3 figures. Minor changes. Published versio

Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation

Abstract We study operator insertions into 1/2 BPS Wilson loops in N $$\mathcal{N}$$ = 6 ABJM theory and investigate their two-point correlators. In this framework, the energy emitted by a heavy moving probe can be exactly obtained from some two-point coefficients of bosonic and fermionic insertions. This allows us to confirm an early proposal [1] for computing the Bremsstrahlung function in terms of certain supersymmetric circular Wilson loops, whose value might be accessible to localization techniques. In the derivation of this result we also elucidate the structure of protected multiplets in the relevant superconformal defect theory and perform an explicit two-loop calculation