Description
It is known that relativistic string theory in AdS5xS5 is integrable, as it admits a Lax pair (classical integrability) and an R-matrix (quantum integrability). The property of being integrable opened the road to many powerful applications which allowed to compute observables, such as the spectrum, useful in making impressive quantitative checks of the AdS5/CFT4 correspondence. Integrability of relativistic string theory also extends to symmetric space backgrounds, where AdS5xS5 is a particular example. The question we pose is: How much do we know about integrability in non-relativistic string theory? In this talk I will report on recent progress in understanding classical integrable structures present in non-relativistic string theory propagating in string Newton-Cartan AdS5xS5. I will elaborate on the coset construction of the non-relativistic action, present the Lax pair associated with its equations of motion and discuss a preliminary work on constructing a spectral curve. This talk is based on work done in collaboration with J. Nieto, O. Ohlsson Sax, A. Torrielli, S. van Tongeren.
