The reason why there is not a direct equivalent to string theory for quantum field theory (QFT) lies in the fundamental differences between these two frameworks and their goals in describing the fundamental nature of reality.
Quantum field theory is a powerful framework that combines quantum mechanics with special relativity to describe the behavior of elementary particles and their interactions. It treats particles as excitations of quantum fields that permeate spacetime. QFT has been remarkably successful in predicting and explaining a wide range of phenomena, particularly in the realm of particle physics.
On the other hand, string theory goes beyond the framework of QFT by postulating that the fundamental constituents of the universe are not point-like particles but rather tiny, one-dimensional objects called strings. These strings vibrate at different frequencies and modes, producing the different particles we observe. String theory aims to provide a unified description of all known fundamental forces, including gravity, and offers a potential framework for reconciling quantum mechanics with general relativity.
The reason why there is not a direct equivalent of string theory for QFT is that they are fundamentally different approaches. String theory introduces new concepts and structures that are not present in QFT, such as extended objects (strings) and higher-dimensional spacetime. It requires a different mathematical framework and set of tools for its formulation and analysis.
While QFT has been extensively tested and validated through experiments, string theory has not yet been experimentally confirmed. It is still an active area of research, and its full theoretical framework is not yet fully understood. Despite its promise, the mathematical complexity and the lack of experimental evidence make it challenging to establish a direct equivalent to string theory within the framework of QFT.
Nevertheless, it is worth noting that there are connections between string theory and certain aspects of QFT. For instance, string theory provides insights into the behavior of strongly interacting systems via holography, a duality known as the AdS/CFT correspondence. This has led to important discoveries and advances in our understanding of both string theory and QFT.