N=1 and N=2 Geometry from Fluxes
By F. Cachazo, C. Vafa. 2002
165 citations recorded by the source corpus.
We provide a proof of the equivalence of N=1 dynamics obtained by deforming N=2 supersymmetric gauge theories by addition of certain superpotential terms, with that of type IIB superstring on Calabi-Yau threefold geometries with fluxes. In particular we show that minimization of the superpotential involving gaugino fields is equivalent to finding loci where Seiberg-Witten curve has certain factorization property. Moreover, by considering the limit of turning off of the superpotential we obtain the full low energy dynamics of N=2 gauge systems from Calabi-Yau geometries with fluxes.
Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/2105809b5fda3af21e7da7725bb1ded7a3915779
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Citations in the corpus
- Chiral Rings and Anomalies in Supersymmetric Gauge Theory (2002, methodology): “For example, we determine the classical relations and quantum deformations of the chiral ring of N = 1 super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.”
- Matrix models, topological strings, and supersymmetric gauge theories (2002, background): “In fact the results of N = 2 Seiberg-Witten geometry was recovered in [15] by considering such a distribution of eigenvalues in the limit W → ǫW as ǫ → 0.”
- Gravitational corrections in supersymmetric gauge theory and matrix models (2002, background): “g [ 17 ]. One can check [16] that the τij computed in the matrix model lead to the right result for τ in the N = 2 theory.”
- Chiral Rings and Phases of Supersymmetric Gauge Theories (2003, methodology): “As in [7], in order to study the theory at a generic point in M, we deform it with a generic superpotential W (Φ) of degree N + 1.”
- Perturbative analysis of gauged matrix models (2002, unknown): “The basic idea of [26] is to deform N = 2 theory to N = 1 by a polynomial tree-level superpotential W (x), which freezes the eigenvalues of the adjoint field Φ to a particular point on the Coulomb branch.”
- Matrix models, geometric engineering and elliptic genera (2003, methodology): “Since in this paper we would be mostly interested in the N = 2 aspects of the theory, we will mainly keep track of the geometry of the curve because it is a feature that survives the limit when the superpotential is turned off and so pertains to the N = 2 theory [17].”
- A Perturbative Window into Non-Perturbative Physics (2002, background): “This unexpected result, that follows straightforwardly from string theory, is completely in accord with field theory arguments, as was shown in [10,17].”
- All Loop Topological String Amplitudes from Chern-Simons Theory (2002, background): “Then the large N dual of this system in type IIB is proposed in [17] (and further elaborated recently in [62]) to be given by propagation in the non-compact Calabi-Yau given by the hypersurface inC(4): uv + y(2) + g(2)(x(2) −m(2))(2) + g(2)Λ(4) = 0”
- Instanton Counting and Chern-Simons Theory (2002, background): “We will restrict ourselves to the case of SU(2) gauge symmetry and only discuss the relevant CY3-folds for this case.”
- On geometry and matrix models (2002, background): “As explained in [11] it is indeed possible to extract the geometry of the N = 2 solution from the effective superpotential of the N = 1 deformation of N = 2 theory and thereby, indirectly, from the associated matrix model.”