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André LeClair

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André LeClair is a Canadian-American physicist and academic. He is a Professor at the Cornell University.[1]

André LeClair
Born
Madawaska, Maine
NationalityCanadian-American
Occupation(s)Physicist and academic
AwardsNational Young Investigator Award, NSF (1993)
Alfred P. Sloan Foundation Fellowship (1992)
Academic background
EducationB.S., Physics
Ph.D., Physics
Alma materMassachusetts Institute of Technology
Harvard University
ThesisBS Thesis: Compton Scattering off Quarks
Ph.D. Thesis: String Field Theory
Academic work
InstitutionsCornell University

LeClair is the recipient of the National Young Investigator Award from the National Science Foundation. He is most known for his work on quantum field theory and integrability, primarily focusing on quantum group symmetries, finite temperature field theory, disordered systems, physics of the Riemann Hypothesis and the cosmological constant.[2]

Education

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LeClair completed his Bachelor of Science in Physics from the Massachusetts Institute of Technology in 1982. 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.[1]

Career

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LeClair began his academic career in 1987 at Princeton University as a Research Associate and remained there until 1989. In 1989, he joined Cornell University, where he held various positions, including Assistant Professor from 1989 to 1995 and Associate Professor from 1995 to 2001. He has been serving as a Professor of Physics at Cornell University for over two decades.[1]

Research

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LeClair's quantum and classical physics research has won him the 1992 Alfred P. Sloan Foundation Fellowship.[3] He has authored numerous publications spanning the areas of quantum field theory, string theory, integrability, number theory, and quantum groups.[4]

Quantum field theory and quantum groups

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LeClair's quantum field theory and quantum groups research have contributed to the identification of new types of quantum group symmetries. Focusing his research efforts on quantum group symmetries in two-dimensional quantum field theory, his work presented a systematic approach for expanding the symmetrical properties of a provided S-matrix[5] and introduced non-local conserved currents within the framework of two-dimensional quantum field theories, along with Denis Bernard.[6] In his examination of quantum affine symmetry,[7] he conducted a comprehensive examination of multiplicative representations of the Yangian double in collaboration with Bernard and Feodor Smirnov, and presented a geometric interpretation for the quantum double.[8] In related research, he investigated the S-matrices of integrable perturbations in N=2 superconformal field theories and obtained the Smatrix by employing the quantum group restriction of the affine Toda theories.[9]

Integrability

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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. He also introduced fractional super soliton field theories, which are integrable and distinguished by a dual interplay of two fractional supersymmetries.[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.[11] His research on the integrability of coupled conformal field theories analyzed the Dynkin diagrams of coupled minimal models and provided a comprehensive conceptual structure for investigating the on-shell dynamics of interconnected conformal field theories. In addition, he proposed a comprehensive approach to the development of integrable defect theories through the application of perturbation techniques to conformal field theory and presented a formal framework for calculating correlation functions at finite temperatures in integrable quantum field theories which is commonly referred to as the LeClair-Mussardo formula.[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.[13]

Statistical mechanics

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LeClair's statistical mechanics research has had numerous implications for the field of theoretical physics.[14] He discovered the first examples of quantum field theories with cyclic renormalization group flows. 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.[15] Dedicating his research efforts towards the statistical mechanics of gases, he presented multiple approaches, including the "Formalism" for quantum statistical mechanics of gases in any dimension, as well as the S-matrix approach to quantum gases in the unitary limit, particularly in two and three spatial dimensions.[16] In his assessment of the limitations and powers of the conformal bootstrap for two conformal theories, polymers and percolation, his study presented approximate numerical exponents, which, while reasonably accurate, fell short of the precision achieved by alternative methodologies like εexpansion or Monte-Carlo simulations.[17] While investigating the deformation of the Ising model and its ultraviolet completion, his study established that such deformations are generally incomplete in the UV due to square-root singularities in the ground state energy. Moreover, the study also proposed including an infinite number of additional irrelevant perturbations to complete the theory.[18] His study on the Ising model with a Majorana fermion spectrum revealed that a complete classification of integrable UV completions consists of only two possibilities, each with supersymmetry. He has also extended the Wigner-Dyson classification of random hamiltonians to non-hermitian hamiltonians, which recently have seen many applications to open quantum systems.

The Riemann Hypothesis and Physics

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LeClair has proposed two approaches towards understanding the validity of the Riemann Hypothesis based on physics. One is based on the universal exponent 1/2 for random walks, which is exactly the real part of the non-trivial zeros.[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.[21]

Awards and honors

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  • 1992 – Fellowship, Alfred P. Sloan Foundation[3]
  • 1993 – National Young Investigator Award, National Science Foundation

Selected articles

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  • LeClair, A. (1989). Restricted sine-Gordon theory and the minimal conformal series. Physics Letters B, 230(1–2), 103–107.
  • LeClair, A., Peskin, M. E., & Preitschopf, C. R. (1989). String field theory on the conformal plane (I).: Kinematical Principles. Nuclear Physics B, 317(2), 411–463.
  • Ahn, C., Bernard, D., & LeClair, A. (1990). Fractional supersymmetries in perturbed coset CFTs and integrable soliton theory. Nuclear Physics B, 346(2–3), 409–439.
  • Bernard, D., & LeClair, A. (1991). Quantum group symmetries and non-local currents in 2D QFT. Communications in mathematical physics, 142, 99–138.
  • LeClair, A., & Vafa, C. (1993). Quantum affine symmetry as generalized supersymmetry. Nuclear Physics B, 401(1–2), 413–454.
  • LeClair, A., & Mussardo, G. (1999). Finite temperature correlation functions in integrable QFT. Nuclear Physics B, 552(3), 624–642.
  • LeClair, A., Román, J. M., & Sierra, G. (2003). Russian doll renormalization group and Kosterlitz–Thouless flows. Nuclear physics B, 675(3), 584–606.

References

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  1. ^ a b c "Andre Leclair | Department of Physics". physics.cornell.edu.
  2. ^ "Physicist offers new take on million-dollar math problem".
  3. ^ a b "LeClair, Andre – Sloan Research Fellows 1955–2007" (PDF).
  4. ^ "Andre Leclair". scholar.google.com.
  5. ^ LeCLair, A.; Smirnov, F. (May 20, 1992). "Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field Theory". International Journal of Modern Physics A. 07 (13): 2997–3022. arXiv:hep-th/9108007. doi:10.1142/S0217751X92001332. S2CID 119328819.
  6. ^ Bernard, Denis; LeClair, André (November 1, 1991). "Quantum group symmetries and non-local currents in 2D QFT" (PDF). Communications in Mathematical Physics. 142 (1): 99–138. doi:10.1007/BF02099173. S2CID 119026420 – via Springer Link.
  7. ^ LeClair, A.; Vafa, C. (July 25, 1993). "Quantum Affine Symmetry as Generalized Supersymmetry". Nuclear Physics B. 401 (1–2): 413–454. arXiv:hep-th/9210009. doi:10.1016/0550-3213(93)90309-D. S2CID 15820663.
  8. ^ Bernard, D.; LeClair, A. (July 25, 1993). "The Quantum Double in Integrable Quantum Field Theory". Nuclear Physics B. 399 (2–3): 709–748. arXiv:hep-th/9205064. doi:10.1016/0550-3213(93)90515-Q. S2CID 16281645.
  9. ^ LeClair, A.; Nemeschansky, D.; Warner, N. P. (February 25, 1993). "S-matrices for Perturbed N=2 Superconformal Field Theory from quantum groups". Nuclear Physics B. 390 (3): 653–680. arXiv:hep-th/9206041. doi:10.1016/0550-3213(93)90493-9. S2CID 11009534.
  10. ^ Ahn, C.; Bernard, D.; Leclair, A. (December 17, 1990). "Fractional supersymmetries in perturbed coset CFTs and integrable soliton theory". Nuclear Physics B. 346 (2): 409–439. doi:10.1016/0550-3213(90)90287-N.
  11. ^ Leclair, A.; Mussardo, G.; Saleur, H.; Skorik, S. (1995). "Boundary energy and boundary states in integrable quantum field theories". Nuclear Physics B. 453 (3): 581–618. arXiv:hep-th/9503227. doi:10.1016/0550-3213(95)00435-U. S2CID 14563728.
  12. ^ Leclair, A.; Mussardo, G. (July 25, 1999). "Finite Temperature Correlation Functions in Integrable QFT". Nuclear Physics B. 552 (3): 624–642. arXiv:hep-th/9902075. doi:10.1016/S0550-3213(99)00280-1. S2CID 14493970.
  13. ^ Ahn, Changrim; LeClair, André (August 18, 2022). "On the classification of UV completions of integrable $T \bar{T}$ deformations of CFT". Journal of High Energy Physics. 2022 (8): 179. arXiv:2205.10905. doi:10.1007/JHEP08(2022)179. S2CID 248986271.
  14. ^ LeClair, Andre; Sierra, German (August 17, 2004). "Renormalization group limit-cycles and field theories for elliptic S-matrices". Journal of Statistical Mechanics: Theory and Experiment. 2004 (8): P08004. arXiv:hep-th/0403178. doi:10.1088/1742-5468/2004/08/P08004. S2CID 250675574.
  15. ^ Anfossi, Alberto; LeClair, André; Sierra, Germán (May 27, 2005). "The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity". Journal of Statistical Mechanics: Theory and Experiment. 2005 (5): P05011. arXiv:cond-mat/0503014. doi:10.1088/1742-5468/2005/05/P05011. S2CID 119442524 – via CrossRef.
  16. ^ How, Pye-Ton; LeClair, Andre (March 26, 2010). "S-matrix approach to quantum gases in the unitary limit I: the two-dimensional case". Journal of Statistical Mechanics: Theory and Experiment. 2010 (3): P03025. arXiv:1001.1121. doi:10.1088/1742-5468/2010/03/P03025. S2CID 115172658.
  17. ^ Leclair, André; Squires, Joshua (2018). "Conformal bootstrap for percolation and polymers". Journal of Statistical Mechanics: Theory and Experiment. 2018 (12). arXiv:1802.08911. doi:10.1088/1742-5468/aaf10a. S2CID 73674896.
  18. ^ "TT¯ deformation of the Ising model and its ultraviolet completion". arXiv:2107.02230. doi:10.1088/1742-5468/ac2a99. S2CID 235743001.
  19. ^ Leclair, André; Mussardo, Giuseppe (2019). "Generalized Riemann hypothesis, time series and normal distributions". Journal of Statistical Mechanics: Theory and Experiment. 2019 (2): 023203. arXiv:1809.06158. doi:10.1088/1742-5468/aaf717. S2CID 119269121.
  20. ^ Mussardo, Giuseppe; LeClair, Andre (November 1, 2021). "Randomness of Mobius coefficents and brownian motion: growth of the Mertens function and the Riemann Hypothesis". Journal of Statistical Mechanics: Theory and Experiment. 2021 (11): 113106. arXiv:2101.10336. doi:10.1088/1742-5468/ac22fb. S2CID 244431965.
  21. ^ França, Guilherme; LeClair, André (August 25, 2015). "Transcendental equations satisfied by the individual zeros of Riemann $\zeta$, Dirichlet and modular $L$-functions". Communications in Number Theory and Physics. 9 (1): 1–50. arXiv:1502.06003. doi:10.4310/CNTP.2015.v9.n1.a1. S2CID 96426525.
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