LQG-Strings, Part 2: Quantizing the worldsheet and appearance of fermions, Nov 11, 2023 скачать в хорошем качестве

LQG-Strings, Part 2: Quantizing the worldsheet and appearance of fermions, Nov 11, 2023

Discussion with Luigi Sousa on how fermions necessarily appear in the worldsheet effective action. Starting with a 2D surface embedded in spin-network state, I describe how the description of punctures of that surface by edges of the spin-networks takes the form of the a spin Hamiltonian. The lowest order term simply corresponds to the total area (if we take the area quantum to be proportional to j, rather than to \sqrt{j(j+1)). The next simplest term is an Ising interaction term whose continuum limit in 2D is a theory of massless Majorana fermions. We further discuss the role of background gauge fields and how they should couple with the string worldsheet. As an aside I outline arguments by Braunstein, Ghosh and Severini according to which it is sufficient to consider regular spin-network graphs (where each vertex has the same degree - the number of edges connected to that vertex) with each edge labeled by j = spin 1/2. Finally I outline how the effective worldsheet action can be understood as arising as a low-energy limit of the system: Surface + Spin-network, and how the semiclassical gravity action (in the connection formulation) can be viewed as arising from low-energy limit of the effective string action. This is work in progress and these ideas are tentative though grounded in physical reasoning and the mathematical structure of the respective theories.