I am a PhD student in DESY (Deutsches Elektronen-Synchrotron) in Hamburg, where I study mathematical physics. In particular, I am interested in the formal structures that arise in the context of string theory and exactly solvable models. You can find out more about me and my interests below.
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
Together with. Drs. Till Bargheer, Carlos Bercini, Andrea Cavaglia', Alexandre Homrich, Paul Ryan and Pedro Vieira 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
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
Despite not being an extraordinary sporty person, I love to follow sports, especially the ones involving some very good italians in it. In the past years, our national athletics team became very good, especially in the 2021 Tokyo Olimpics and in the 2024 European Championships in Rome. Moreover, I started to follow closer tennis matches since the italians in the top 100 are doing very good, especially Jannik Sinner (atm world 1st!) Jasmine Paolini (atm world 7th) and Lorenzo Musetti. My favourite player is Matteo Berrettini (world 6th in 2022). This tennis closer look was strongly encouraged since one of my closest friends became a tennis instructor with his own tennis school near my village in Piedmont. About our national football team... well, let's not talk about this for a while.
I try to work only in linux OS environments. A reddit post that contains some comments of a newbie Linux user that I like is:
Switching to a Linux distro made me enjoy using a PC more (just some appreciation lol)
byu/FleuramdcrowAJ inlinux
A free-to-use work management system that I use a lot since I am in Hamburg is git. No idea on what git is? Check this out:
I don’t understand how to use git
byu/Ok-Dot6854 ingit
What is your default branch name?
byu/manuchehr_me ingit
Comment
byu/manuchehr_me from discussion
ingit
As you can guess from this website, I love to work/visualise concepts in a text-only environment. There are some good reasons to work (sometimes) in tty mode only, see for example this nice discussion here.
desy.de/~dlai: [2022 -- present] Graduate Research Assistant -- DESY -- Hamburg (DEU)
desy.de/~dlai: [2021 -- 2022] Math and Physics High School Teacher -- Liceo Statale Vasco Beccaria Govone -- Mondovi (IT)
desy.de/~dlai: [2021 -- 2021] Student Aide -- Universita' degli Studi di Torino -- Torino (IT)
desy.de/~dlai: [2021 -- 2021] Math and Science Middle School Teacher -- IC Luigi Einaudi -- Dogliani (IT)
desy.de/~dlai: [2019 -- 2021] Research and Development Scientist -- UR Fog -- San Mauro Torinese (IT)
desy.de/~dlai: [2019 -- 2021] MSc. in Theoretical Physics -- Universita' degli Studi di Torino -- Torino (IT)
desy.de/~dlai: [2016 -- 2019] BSc. in Physical Chemistry -- Universita' degli Studi di Torino -- Torino (IT)
desy.de/~dlai: [2011 -- 2016] High School Diploma -- Liceo Statale Vasco Beccaria Govone -- Mondovi (IT)
desy.de/~dlai: mail: davide.lai@desy.de
desy.de/~dlai: office: Geb. 2a, DESY, Notkestraße 85 -- 22607 Hamburg