Chaos in Hadronic Matter: Holographic Insights from Quantum Field Theory.

Research utilising holographic modelling reveals chaos functions as an order parameter detecting symmetry breaking in gauge theory. Numerical analysis of orbits and out-of-time-ordered correlators (OTOCs) identifies a critical temperature influencing chaotic behaviour, aligning with Lyapunov exponent analysis and suppressing growth with increasing energy.

The behaviour of strongly interacting systems, such as those found within the cores of atomic nuclei and in the quark-gluon plasma created during heavy-ion collisions, remains a significant challenge for theoretical physics. Recent research explores the connection between chaotic dynamics and the underlying structure of these systems, utilising the holographic principle – a conjecture linking gravity and quantum field theory. A new study by Lia et al. investigates chaos within simplified models, known as holographic matrix models, designed to mimic the behaviour of mesons and baryons – composite particles made of quarks and gluons. Their work, titled ‘Chaos in the holographic matrix models for meson and baryon’, employs numerical and analytical techniques to characterise chaotic behaviour, potentially identifying a link between the emergence of chaos and the spontaneous breaking or restoration of symmetry in the underlying quantum field theory. The research originates from a collaboration between Si-wen Lia of Dalian Maritime University, and Xun Chen from both the INFN (Istituto Nazionale di Fisica Nucleare) in Bari and the University of South China.

Investigations into matrix models – simplified representations of Quantum Chromodynamics (QCD) – reveal the emergence of chaotic behaviour and offer a novel approach to understanding the strong force. These models, used to describe hadrons – composite particles such as mesons and baryons – are now being analysed using tools traditionally employed in the study of classical chaos, bolstered by the principles of the holographic duality known as the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence.

QCD describes the strong interaction, one of the four fundamental forces of nature, governing the interactions between quarks and gluons. Calculations within QCD become exceptionally difficult in the non-perturbative regime – situations where the interaction strength is large, preventing the use of standard approximation techniques. Matrix models offer a pathway to circumvent these difficulties.

Researchers are employing techniques from classical chaos theory, such as the construction of Poincaré sections – geometric tools used to visualise the behaviour of dynamical systems – and the calculation of Lyapunov exponents – which quantify the rate of separation of infinitesimally close trajectories, indicating sensitivity to initial conditions and thus chaos. Numerical calculations reveal potential phase structures within these models, suggestive of transitions between different states of matter or symmetry breaking/restoration within the underlying gauge theory – the mathematical framework describing the strong interaction.

Crucially, these classical analyses are being linked to measures of quantum chaos. Out-of-Time-Ordered Correlators (OTOCs) – quantities that measure the degree to which quantum operators fail to commute at different times – serve as a proxy for the scrambling of information in a quantum system, and are considered a hallmark of quantum chaos. Researchers demonstrate that OTOCs exhibit saturation beyond a critical temperature, mirroring the behaviour observed in classical chaotic systems.

Analytical derivations further reveal that OTOCs are suppressed by the growth of a specific parameter within the matrix model, providing insight into the underlying dynamics driving this behaviour. This suppression suggests a connection between the rate of information scrambling and the fundamental parameters governing the strong interaction.

This convergence of classical and quantum analyses strengthens the hypothesis that chaotic dynamics are intrinsic to the matrix model framework and, by extension, potentially to the strong interaction itself. The observed correlation between Lyapunov exponents, OTOC saturation, and potential phase transitions hints at a unifying principle governing complex systems.

Future research will focus on extending these analyses to more complex matrix model configurations, incorporating additional degrees of freedom and exploring the effects of different background geometries. This will allow researchers to probe the non-perturbative regime of QCD with greater precision and potentially reveal new insights into the fundamental nature of the strong force.