Large charge and perturbation theory

In this talk, I will explore the applications of the semiclassical method, specifically focusing on the large charge expansion within the context of the asymptotically safe Litim–Sannino model. This model is significant in theoretical physics as it provides insights into quantum field theories that exhibit asymptotic safety, a concept that suggests the existence of a non-trivial ultraviolet fixed point.

To begin, I will delve into the perturbative aspects of the calculations associated with this model. This involves examining the behavior of the system under small perturbations and how these perturbations influence the overall dynamics and properties of the model. I will discuss the mathematical techniques employed to perform these calculations and highlight key results that emerge from this perturbative analysis.

Following this, I will identify the lowest-lying operator within the framework of the large charge expansion. This operator plays a crucial role in understanding the dynamics of the theory, particularly in relation to its symmetry properties and its implications for physical observables. I will also investigate the analytic structure of the large charge expansion itself, shedding light on how this structure informs our understanding of the model's behavior at different energy scales.

Furthermore, I will apply these findings to various proposed dualities at the critical point of the Litim–Sannino model. These dualities are essential for establishing connections between seemingly disparate physical theories and can provide deeper insights into their underlying structures. I will discuss how the results obtained from the semiclassical method and large charge expansion can be leveraged to test and refine these duality proposals.

Overall, this talk aims to provide a comprehensive overview of how semiclassical techniques and large charge expansions can enhance our understanding of the asymptotically safe Litim–Sannino model, with implications for broader areas in quantum field theory and theoretical physics.