Quantum field theory (QFT) is a rich and active area of research with several open problems that researchers are currently working on. Here are some examples of ongoing research directions and open problems in QFT:
Ultraviolet (UV) Divergences: One of the major challenges in QFT is the presence of UV divergences, which arise when trying to calculate certain quantities. Developing rigorous and systematic methods to handle and eliminate these divergences, such as renormalization techniques, is an ongoing research effort.
Non-perturbative QFT: Perturbative methods are well-developed for weakly interacting quantum field theories. However, understanding non-perturbative aspects, such as the strong coupling regime and the emergence of bound states, remains a challenge. Researchers are exploring techniques like lattice QFT, supersymmetry, and dualities to address these non-perturbative aspects.
Quantum Gravity: The unification of quantum theory and general relativity is one of the outstanding problems in theoretical physics. Researchers are actively investigating various approaches to quantum gravity, such as string theory, loop quantum gravity, and asymptotic safety, in an attempt to develop a consistent quantum theory of gravity.
Gauge/Gravity Correspondence: The gauge/gravity correspondence, also known as the AdS/CFT correspondence, is a conjectured duality between certain quantum field theories and gravity in higher-dimensional anti-de Sitter space. Understanding the precise details of this correspondence and extending it to more realistic physical scenarios is an active area of research.
Integrability and Exact Solvability: Finding solvable models in QFT and understanding their underlying integrable structures have been fruitful areas of research. Researchers are exploring exactly solvable QFTs, integrability in AdS/CFT, and applications to condensed matter systems, hoping to gain insights into the broader field of QFT.
Symmetries and Dualities: Symmetry plays a crucial role in QFT, and researchers are continually exploring various symmetries and their implications. Studying the interplay of different symmetries, such as supersymmetry, conformal symmetry, and topological symmetry, and uncovering new dualities between different QFTs are active research directions.
These are just a few examples, and there are many more open problems and exciting research directions in the field of quantum field theory. The active and dynamic nature of research in QFT ensures that new problems and challenges continue to arise, stimulating further investigation and progress.