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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SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2025)162 |
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| author | Mendel Nguyen Mithat Ünsal |
| author_facet | Mendel Nguyen Mithat Ünsal |
| author_sort | Mendel Nguyen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2a1e97a2f05c4c5b83dae6e4b6ab97c7 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-2a1e97a2f05c4c5b83dae6e4b6ab97c72025-08-20T02:17:01ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025315010.1007/JHEP03(2025)162Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetryMendel Nguyen0Mithat Ünsal1Department of Physics, North Carolina State UniversityDepartment of Physics, North Carolina State UniversityAbstract 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.https://doi.org/10.1007/JHEP03(2025)162Nonperturbative EffectsSigma ModelsSolitons Monopoles and Instantons |
| spellingShingle | Mendel Nguyen Mithat Ünsal Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetry Journal of High Energy Physics Nonperturbative Effects Sigma Models Solitons Monopoles and Instantons |
| title | Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetry |
| title_full | Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetry |
| title_fullStr | Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetry |
| title_full_unstemmed | Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetry |
| title_short | Refined instanton analysis of the 2D CP N−1 model: mass gap, theta dependence, and mirror symmetry |
| title_sort | refined instanton analysis of the 2d cp n 1 model mass gap theta dependence and mirror symmetry |
| topic | Nonperturbative Effects Sigma Models Solitons Monopoles and Instantons |
| url | https://doi.org/10.1007/JHEP03(2025)162 |
| work_keys_str_mv | AT mendelnguyen refinedinstantonanalysisofthe2dcpn1modelmassgapthetadependenceandmirrorsymmetry AT mithatunsal refinedinstantonanalysisofthe2dcpn1modelmassgapthetadependenceandmirrorsymmetry |