Later in 1987, he obtained a Ph.D. in Physics from Harvard University under the guidance of Michael Peskin, with their collaborative research focusing on string theory.
[9] LeClair's early research presented an examination of the sine-Gordon theory's Hilbert space and proposed a method to impose limitations on it while maintaining integrability by leveraging the quantum group structure.
[10] In a collaborative study with Giuseppe Mussardo and others, he developed a novel approach named "Rchannel TBA" to analyze the ground state energy of scalar integrable quantum field theories with boundaries.
[12] More recently in 2022, his work suggested a systematic approach to classifying and understanding UV completions of 2D CFTs deformed by irrelevant TT perturbations and provided specific examples and results for the Ising model and other cases with different symmetries.
In connection with this, he studied the Russian doll BCS model of superconductivity and established the presence of energetically elevated Cooper pairs, and possessed an interpretation within the framework of the renormalization group.
[19][20] In another approach he established the result that if there is a unique solution for every integer to the Franca-LeClair equation, then the Riemann Hypothesis is true.
More recently he has constructed a physical model a fermion scattering with impurities whose quantized energies satisfy a Bethe ansatz equation which exactly correspond to the Riemann zeros.