A Geometric unification of dualities

By F. Cachazo, B. Fiol, K. Intriligator, Sheldon Katz, C. Vafa. 2001

331 citations recorded by the source corpus.

Abstract We study the dynamics of a large class of N =1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi–Yau three-folds. These include N =2 (affine) A - D - E quiver theories deformed by superpotential terms, as well as chiral N =1 quiver theories obtained in the presence of vanishing 4-cycles inside a Calabi–Yau. We consider the various possible geometric transitions of the 3-fold and show that they correspond to Seiberg-like dualities (represented by Weyl reflections in the A - D - E case or “mutations” of bundles in the case of vanishing 4-cycles) or large N dualities involving gaugino condensates (generalized conifold transitions). Also duality cascades are naturally realized in these classes of theories, and are related to the affine Weyl group symmetry in the A - D - E case.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/db0199076e69cdfb4ca88d1f1b97c6447d0e66ec

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Citations in the corpus

Building the standard model on a D3-brane (2005, background): “A useful subclass of mutations has the physical interpretation of Seiberg duality [32, 43]: the N = 1 supersymmetric gauge theories corresponding to the original and mutated set of fractional branes are each others Seiberg dual.”
Les Houches lectures on matrix models and topological strings (2004, background): “branes wrapping two-spheres [16, 14], and the string field theory description reduces to the ADE matrix models considered in [46].”
Symmetries of Toric Duality (2002, methodology): “Subsequently, as Seiberg duality is Picard-Lefshetz monodromy [13], it is reasonable to expect that toric duality, as a consequence of multiplicity permutation, should lead to Seiberg duality.”
Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “For k > 2, the theory is studied in [14].”
Seiberg Duality for Quiver Gauge Theories (2002, methodology): “Recently, several groups [6, 13, 29] have shown that Seiberg dual pairs or even sets of theories can be obtained in this framework, using the procedure of “partial resolution” [50].”
Topological Strings and Integrable Hierarchies (2003, methodology): “In particular if one is interested in having functions of the form H(p, x) = pr + xs + lower order terms then one can take an Ar−1 quiver matrix theory (with adjoint matrices at the r− 1 nodes and bifundamental for edges) and tune the potential for the adjoints suitably.”
Direct mediation of metastable supersymmetry breaking (2006, methodology): “We can also T-dualize the NS5 branes to turn the D4 branes suspended between the NS5 branes into D branes wrapping compact cycles in a local Calabi-Yau manifold [54].”
Supersymmetry Breaking from a Calabi-Yau Singularity (2005, background): “However, in general there are fewer than n complex structure deformations [34].”
Obstructions to the Existence of Sasaki–Einstein Metrics (2006, background): “Thus an initial reaction [18] is that one has found agreement between geometric and field theory results.”
Matrix models, topological strings, and supersymmetric gauge theories (2002, background): “As a further generalization one can consider the topological lift of the models considered in [14].”
Quivers, tilings, branes and rhombi (2005, background): “These “phases” of the theory are believed to be Seiberg–dual to each other [55, 56, 57, 58].”
Dimer models and toric diagrams (2005, methodology): “Indeed a few methods, different and even faster than the inverse algorithm of [9], were used in the literature to compute the matter content of the quiver theory: using (p,q) webs [13], Ext groups [12], exceptional collections [14], and others.”
GUTs and exceptional branes in F-theory — II. Experimental predictions (2008, background): “The condition that all gauge theory anomalies must cancel is equivalent to the requirement that in a consistent bound state of D3-, D5- and D7-branes, the total RR flux measured over a compact cycle must vanish [94].”
$\mathcal{N} = 2$ quantum field theories and their BPS quivers (2011, background): “• The relation of the 4d quivers with the soliton spectrum in 2d [17] was studied in various places, see for example [14, 34, 51], more recently this 2d/4d correspondence and the associated construction of BPS quivers was discussed in [16].”
On geometry and matrix models (2002, background): “In the case of an Ar quiver there is a more straightforward description of the saddle points [7,8,9].”