2023/09/21 by Mendel Nguyen, Nguyen, Mendel, Mithat Ünsal +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum many-body systems #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2309.12178
openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address nonperturbative dynamics of the two-dimensional bosonic and supersymmetric ℂPN-1 models for general N by developing new tools directly on ℝ2. The analysis starts with a new formulation of instantons that is consistent with the existence of the classical moduli space, classical dipole--dipole type interactions of instanton--anti-instanton pairs, and vanishing interaction of instanton--instanton pairs. The classical consistency is achieved via a representation of the instanton as a collection of N pointlike constituents carrying pair of real and imaginary charges valued in the weight lattice of SU(N). The constituents interact via a generalized Coulomb interaction and do not violate the fact that instanton is a single lump with integer topological charge. By developing the appropriate Gibbs distribution, we show that the vacuum can be captured by a statistical field theory of these constituents, and their cluster expansion. Contrary to the common belief that instantons do not capture the vacuum structure and non-perturbation properties of such theories, our refined analysis is able to produce properties such as mass gap, theta dependence, and confinement of the theory on ℝ2. In supersymmetric theory, our construction gives a new derivation of the mirror symmetry between the sigma model and the dual Landau--Ginzburg model by Hori and Vafa. Our construction also demonstrates that there is absolutely no conflict between large N and instantons.