On classification ofN=2 supersymmetric theories

Abstract

We find a relation between the spectrum of solitons of massive N = 2 quantum field theories in d = 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 symmetric N = 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. 11/92

Topological σ-models and the large-N matrix integrals

“…This seems to indicate the equivalence of the CP 1 and the N = 2 supersymmetric sine-Gordon theories at least in their topological versions. The correspondence between these theories have been known for some time based on the agreement of the particle spectra and scattering matrices [12,13]. Our results seem to provide further evidence for their equivalence.…”

“…Thus the topological CP 1 model may be identified with the (topological version of the) N = 2 supersymmetric sine-Gordon theory. The close relation between the CP 1 and N = 2 sine-Gordon models has been noted sometime ago based on the comparison of the particle spectra and S-matrices of these theories [12,13]. In Section 5 we discuss a possible generalization of our construction to other manifolds and formulate a LG description of the topological CP 2 model.…”

A model for gauge theories with Higgs fields

“…For example, both types of theories are known to have similar non-renormalization theorems ( [25], [26]), and both admit topological twists ( [27], [28]). I think that this latter property is particularly significant, because the exact results a la , [2]) are likely to have a semi-topological origin, very much like the exact results one can obtain in two dimensions [29]. Another important fact is that effective superpotentials in two dimensions are very similar to effective prepotentials in four dimensions.…”

A note on domain walls and the parameter space of Script N = 1 gauge theories

“…The set of solutions to the linearised Bogomol'nyi equation about each vacuum defines a cycle △ j in field space, and one can show [40] that by comparing the two cycles △ j and △ k at a given value of t ∈ [0, 1], the number of solutions is given precisely by the intersection number,…”

“…More precisely, we can write the tension of the second wall 10) where the second term is the leading order interaction potential V (r) between the constituent 1-walls positioned at z = z 0 and z = z 0 + r respectively (see The Bogomol'nyi equations decouple in the mass-eigenstate basis for the intermediate vacuum, where M is diagonal. In other words, since M is symmetric, the eigenvalues of the following system [40] 0 e −iγM e iγ M 0 12) are real and paired {m µ , −m µ }, for µ = 1, . .…”