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On classification ofN=2 supersymmetric theories
Open accessAbstract
We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.
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Cites
Principles of Algebraic Geometry
Griffiths, P., & Harris, J. (1994) · Wiley · doi:10.1002/9781118032527 · Cited by 6,765
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Ireland, K., & Rosen, M. (1990) · Graduate texts in mathematics · doi:10.1007/978-1-4757-2103-4 · Cited by 1,311
Singularities of Differentiable Maps
(1988) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-3940-6 · Cited by 1,234
Deligne, P. (1971) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684692 · Cited by 1,019
Variation of hodge structure: The singularities of the period mapping
Schmid, W. (1973) · Inventiones Mathematicae · doi:10.1007/bf01389674 · Cited by 817
Cited by
Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
Seiberg, N., & Witten, E. (1994) · Nuclear Physics B · doi:10.1016/0550-3213(94)90214-3 · Cited by 2,117
Geometry of 2D topological field theories
Dubrovin, B. (1996) · Lecture Notes in Mathematics · doi:10.1007/bfb0094793 · Cited by 1,117
Superstrings and topological strings at large N
Vafa, C. (2001) · Journal of Mathematical Physics · doi:10.1063/1.1376161 · Cited by 498
Self-citationNon-Abelian string junctions as confined monopoles
Shifman, M., & Yung, A. (2004) · Physical Review D · doi:10.1103/physrevd.70.045004 · Cited by 309
Metadata
- Authors
- Cecotti, S., & Vafa, C.
- Venue
- Communications in Mathematical Physics
- Published
- 1993-12
- Volume
- 158
- Issue
- 3
- Pages
- 569-644
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W1978069575
- Cited by
- 432
- References
- 5
- FWCI
- 10.60
- Type
- journal article
- Language
- en
- Open access
- green
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