Non-relativistic Strings from Quantum Mechanics


Harmark, T. (2019). Non-relativistic Strings from Quantum Mechanics. Perimeter Institute. https://pirsa.org/19050026


Harmark, Troels. Non-relativistic Strings from Quantum Mechanics. Perimeter Institute, May. 14, 2019, https://pirsa.org/19050026


          @misc{ pirsa_19050026,
            doi = {},
            url = {https://pirsa.org/19050026},
            author = {Harmark, Troels},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Non-relativistic Strings from Quantum Mechanics},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {may},
            note = {PIRSA:19050026 see, \url{https://pirsa.org}}


This talk is about a new type of string theory with a non-relativistic conformal field theory on the world-sheet, as well as a non-relativistic target space geometry. Starting with the relativistic Polyakov action with a fixed momentum along a non-compact null-isometry, we can take a scaling limit that gives the non-relativistic string, including an interesting intermediate step. This can in particular be applied to a string on AdS5 x S5. In this case the scaling limit realizes a limit of AdS/CFT that on the field theory side gives a quantum mechanical theory known as Spin Matrix theory. We review that Spin Matrix theory is a finite-N version of nearest neighbor spin chains, from which one can find a long-wavelength semi-classical description using sigma-model such as the Landau-Lifshitz sigma-model. Hence, we can show that both sides of the AdS/CFT gives, in this limit, equivalent non-relativistic sigma-models that we are able to write down in a fully covariant manner, and show that it has a non-relativistic local symmetry that realizes the Galilean Conformal Algebra (GCA). This suggests that one has a holographic duality between the quantum mechanical theory of Spin Matrix theory, and the non-relativistic string. This could provide a more tractable holographic duality in which one can study the emergence of non-relativistic strings, geometry and gravity.