String Theory Journal Club

[Note: the seminar will take place in 4.49 lecture room!] How complex is a path integral? In this talk, I will introduce proposals for the gravitational dual of computational cost in holographic field theories. To define terms, in Nielsen's geometric approach, complexity is the length of the shortest path between a reference and target state, while cost is the length of a general, not-necessarily-shortest path. To compare to holographic state complexity proposals, our proposals are different in that: (1) the boundary dual is cost, a quantity that can be optimised to state complexity, (2) our set of proposals is large: all functions on all bulk subregions of any co-dimension which satisfy the physical properties of cost, and (3) the proposals are by construction UV-finite. Lastly, I will explain how the path integrals, which we are proposing the cost of, fit in the framework of holographic $T\bar T$. The talk is based onarXiv:2203.08842.