AdS/CFT
Together with Dr. Till Bargheer and
Dr. Thiago Fleury
we are studying particular regimes
of N = 4 SYM theory in order to compute exactly
various correlation functions in order to test the celebrated
AdS/CFT duality. It is indeed well-known since the early 2000s that is possible to approximate the dynamics of strings moving
in an AdS5 x S5 background to some classes of exactly solvable models, but while the two-point functions are
very-well studied, much less is known about three-point and multi-point functions. Some useful references are:
desy.de/~dlai: [Beisert, N. et al.] 1012.3982
desy.de/~dlai: [Beisert, N.] nlin/0610017
desy.de/~dlai: [Basso, B., Komatsu, S. and Vieira, P.] 1505.06745
desy.de/~dlai: [Fleury, T. and Komatsu, S.] 1611.05577
desy.de/~dlai: [Fleury, T. and Komatsu, S.] 1711.05327
desy.de/~dlai: [Bargheer, T., Coronado, F. and Vieira, P.] 1904.00965
desy.de/~dlai: [Bargheer, T., Coronado, F. and Vieira, P.] 1909.04077
Separation of Variables in Integrable Models
Together with. Drs. Till Bargheer, Carlos Bercini,
Andrea Cavaglia' and Paul Ryan we are trying to extend the separation of variables method (very-well known in
the exactly solvable models' literature) to the context of planar N=4 SYM. In this theory, the spectrum of all the operators is encoded in the
Quantum Spectral Curve (QSC), a set of non-perturbative objects that satisfies some set of finite-difference equations. However, beyond tree-level,
very few is known about the meaningful norms that can be defined in this functional space at any order in the coupling. A complete handling of
scalar products in this space would have some implications in the computations of structure constants in this theory. Some useful references are:
desy.de/~dlai: [Cavaglia', A., Gromov, N. and Levkovich-Maslyuk, F.] 1907.03788
desy.de/~dlai: [Gromov, N., Levkovich-Maslyuk, F. and Ryan, P.] 2011.08229
desy.de/~dlai: [Cavaglia', A., Gromov, N. and Levkovich-Maslyuk, F.] 2103.15800
desy.de/~dlai: [Bercini, C., Homrich, A. and Vieira, P.] 2210.04923
Exact R-Matrices and Quantum Algebras
Another interesting problem is related to the algebraic structure arising in the above-mentioned regimes of string theory/N = 4 SYM. In the planar limit,
the study of the spectrum of the theory revealed a very intriguing relation to Hopf algebras, in particular with the Yangian of centrally-extended su(2|2) Lie
superalgebra. Once that the quasi-co-commutative nature of this algebra is delineated, it is not known how to explicitly build the associated
(universal) R-matrix, that -- translating this object to string theory -- regulates the factorised dynamics for the excitations on the string worldsheet transforming in
any kind of (irreducible) modules of Y(su(2|2)). To have such an explicit construction would be satisfactory and useful to achieve a simplified form of
the R-matrix in some particular kind of representation where is known to be a difficult object to manipulate. Some useful references are:
desy.de/~dlai: [Plefka, J., Spill, F. and Torrielli, A.] hep-th/0608038
desy.de/~dlai: [Arutyunov, G., de Leeuw, M. and Torrielli, A.] 0902.0183
desy.de/~dlai: [Arutyunov, G., de Leeuw, M. and Torrielli, A.] 0903.1833
desy.de/~dlai: [Beisert, N., de Leeuw, M. and Hecht, R.] 1602.04988
desy.de/~dlai: [Beisert, N., and Im, E.] 2210.11150
desy.de/~dlai: [Beisert, N., and Im, E.] 2401.10327