Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetry
Abstract We address nonperturbative dynamics of the two-dimensional bosonic and supersymmetric CP N−1 models for general N by developing new tools directly on R 2. The analysis starts with a new formulation of instantons that is consistent with the existence of the classical moduli space, classical...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2025)162 |
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| Summary: | Abstract We address nonperturbative dynamics of the two-dimensional bosonic and supersymmetric CP N−1 models for general N by developing new tools directly on R 2. 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 R 2. 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. |
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| ISSN: | 1029-8479 |