Chiral Rings and Anomalies in Supersymmetric Gauge Theory
By N. Seiberg. 2002
457 citations recorded by the source corpus.
Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of ``integration constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of = 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.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/e3f03fc3fe6d1fdad36d3dfd8f3ddb3c6bdf3a84
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In Nuclear and High Energy Physics
Citations in the corpus
- Gravity Induced C-Deformation (2003, methodology): “16) As shown in [13] and [17] using direct field theory analysis, the effective superpotential in this case receives contributions only from planar diagrams, consistently with the topological string computation discussed in the above.”
- Large N BPS states and emergent quantum gravity (2005, background): “A good discussion of this can be found in [41].”
- Chiral Rings and Phases of Supersymmetric Gauge Theories (2003, background): “Following [27], only the sphere and disk contribution to the free energy of the corresponding matrix model are relevant.”
- An Index for 4 Dimensional Super Conformal Theories (2005, background): “coupling and strong coupling partition functions agree with each other (see [44] for an explanation).”
- Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, background): “Integrate out the S -field, which amounts to SN = e−τ , a quantum modified chiral ring relation, similar to its 4d counterpart [56].”
- Supersymmetric vacua and Bethe ansatz (2009, background): “It would be nice to derive this from some Ward identities, analogous to the generalized Konishi anomaly [51].”
- Dynamical SUSY breaking in meta-stable vacua (2006, background): “The supersymmetric vacua of this theory have been much studied (see e.g. [ 30-32 ]). We”
- SUPERCONFORMAL FIELD THEORIES (2005, unknown): “In a regime where matter fields are integrated out it is replaced by the generalized Konishi anomaly [11, 22].”
- Liouville Field Theory — A decade after the revolution (2004, methodology): “This may seem rather complicated and less efficient if we are only interested in the double scaling limit, but this method has a lot of applications including the recent Dijkgraaf-Vafa conjecture [90, 91, 92], [93, 94, 95].”
- D3-brane potentials from fluxes in AdS/CFT (2010, unknown): “However, the commutators of the matter fields and Wα vanish in the chiral ring [44], AW (1) α −W (2) α A ∼ W (1) α B −BW (2) α ∼ 0 .”