## Alexander Frenkel L&S Sciences

### UV Completion of Aristotelian Yang-Mills and Topological Methods in HL Gravity

Symmetry is a very important and beautiful tool in physics. From every symmetry in a physical system, one can derive a conserved quantity. However, when one attempts to study various quantum systems with interesting and useful symmetries compatible with Einstein’s Special Theory of Relativity, one finds that some of them fall apart and create divergences at high energies. One method of resolving this problem is to work in a hypothetical space-time where Lorentz symmetry doesn’t have to hold at high energies. This gives us more freedom in building the theory, and makes it easier to complete the theory at high energies. Using this method gives interesting mathematical and physical insights about the theories in question. Our project will be centered around the specific cases of Supersymmetric Yang-Mills (an interesting generalization of electromagnetic theory that is closely connected to the strong nuclear force) and topological Horava-Lifshitz gravity (a theory of gravity that can give interesting mathematical insights about the mathematical concept of Ricci Flow).

#### Message To Sponsor

To The Kwatinetz Fund, My experience this summer has been absolutely amazing. For the past three summers, I've been trying to find serious opportunities in a theoretical lab, and this is the first time I was successful. I was able to work on a theoretical physics project, far from the simulation-based experiences I've had in the past, of the type that I've dreamed of since high school. I learned a ton; a lot of physics and a lot about how physics is done. I've strengthened my resolve to go to graduate school in the field, and to go into academia afterwards. This summer is going to stick with me forever, both as a memory and in the skills and tactics I will use in my future research. Thank you very much, Alexander Frenkel**Major:**Physics

**Mentor:**Petr Horava

**Sponsor:**Kwatinetz Fund