Joint Theory Journal Club: Tamas Gombor

Speaker: Tamas Gombor

Title: Integrable long range spin chains in finite lengths 

Abstract:
The anomalous dimensions of the single-trace operators of the planar N=4 super Yang-Mills theory are equivalent to the energy levels of an integrable long range spin chain as long as the loop order is less than the classical dimension of the operator. For higher orders, wrapping corrections are appeared. For two-point functions, it is already clear how to handle these corrections, but for other physical quantities (like three-point functions) there are unsolved questions.
In this talk I will show a perturbative definition for transfer matrices which give the conserved charges of integrable long range spin chains in the asymptotic limit. The main advantage of this definition is that it is also well defined even for shorter spin chains therefore it gives a procedure for integrability preserving definition of the long range spin chains in finite lengths. We will see that the eigenvalues of these operators are similar in many respects to the wrapping corrections of the anomalous dimensions of the N=4 SYM. I hope that these finite volume long range spin chains could be good toy models of the N=4 SYM and they could serve as ideal playgrounds for tests of ideas for the wrapping corrections.