Quantum Field Theory (QFT) is like the backbone of modern physics. It’s the natural language scientists use to describe particle physics, condensed matter, cosmology, string theory, and even some parts of mathematics like geometry and topology. [Nathan Seiberg](https://scgp.stonybrook.edu/video/video.php?id=389) explains that just like calculus was a breakthrough for understanding motion, QFT is today's essential tool for understanding the fundamental layers of our universe. Yet, despite decades of progress, QFT is still unfinished – messy, evolving, and even hinting that it might need a full reformulation. ### **What I'm Thinking About** - **Three Key Facts:** 1. QFT is not yet mathematically rigorous – unlike calculus, which has been fully formalized. 2. Traditional ways of building QFTs, like using Lagrangians, often fail at strong coupling (where interactions are intense) and in exact solutions. 3. Many important theories either need multiple Lagrangians to be described (due to duality) or don't have any Lagrangian at all. - **Differentiators:** - Lagrangians work beautifully when the theory is weakly coupled, but once things get messy (strong coupling), they lose their power. - In many advanced areas, like topological quantum field theories (TQFTs) and theories without classical limits, we can’t even start with a Lagrangian. - Dualities – when two very different-looking theories actually describe the same physics – show that sticking to one Lagrangian is limiting. - **Interesting Points from Research:** - New structures like "higher-form symmetries" have emerged, describing how not just particles but strings, surfaces, and other extended objects behave. - Strong coupling behaviors often require creative methods like bootstrap techniques, holomorphic tools, and insights borrowed from string theory. - Higher-form symmetries extend how we think about broken and unbroken phases of matter – updating ideas from Landau’s classic theories of phase transitions. ### **So What?** For anyone thinking about the future of physics (or even just curious about where math and physics meet), this talk is a wake-up call. We can’t just rely on old tools like Lagrangians anymore. To solve the deepest problems — like what really happens at strong coupling, or how to truly describe systems without classical analogs — we need fresh thinking. Studying topological observables, exploring higher symmetries, and not being afraid to throw away traditional frameworks might be the keys to the next big breakthroughs. #deeptech