# Non-relativistic Strings from Quantum Mechanics

### APA

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

### MLA

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

### BibTex

@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}} }

## Abstract

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.