PIRSA:19020086

Complexity and RG flow

Bhattacharyya, A. (2019). Complexity and RG flow. Perimeter Institute. https://pirsa.org/19020086

Bhattacharyya, Arpan. Complexity and RG flow. Perimeter Institute, Feb. 27, 2019, https://pirsa.org/19020086 

          @misc{ pirsa_PIRSA:19020086,
            doi = {10.48660/19020086},
            url = {https://pirsa.org/19020086},
            author = {Bhattacharyya, Arpan},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Complexity and RG flow},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020086 see, \url{https://pirsa.org}}
          }

Arpan Bhattacharyya

Indian Institute of Technology Gandhinagar

Talk number
PIRSA:19020086
Collection
Talk Type
Subject
Abstract

Motivated by recent interesting holographic results, several attempts have been made to study complexity ( rather " Circuit Complexity") for quantum field theories using Nielsen's geometric method. But most of the studies so far have been limited to free quantum field theory. In this talk we will take a baby step towards understanding the circuit  complexity for interacting quantum field theories. We will consider \lambda \phi^4 theory and discuss in detail how to set up the computation perturbatively in coupling. Our method enables us to study circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the \phi^4 interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group. Finally we discuss several possible generalization and compare our results with other approaches.