Bipartite field theories, cluster algebras and the Grassmannian

We review recent progress in Bipartite Field Theories. We cover topics such as their gauge dynamics, emergence of toric Calabi-Yau manifolds as master and moduli spaces, string theory embedding, relationships to on-shell diagrams, connections to cluster algebras and the Grassmannian, and applications to graph equivalence and stratification of the Grassmannian.

[1]  S. Fomin,et al.  Cluster algebras IV: Coefficients , 2006, Compositio Mathematica.

[2]  M. Yamazaki,et al.  String theory origin of bipartite SCFTs , 2012, 1211.4587.

[3]  A. Zaffaroni,et al.  THE MASTER SPACE OF N=1 GAUGE THEORIES , 2008, 0801.1585.

[4]  J. Maldacena,et al.  Conformal collider physics: energy and charge correlations , 2008, 0803.1467.

[5]  L. Motl,et al.  Deconstructing (2,0) and Little String Theories , 2001, hep-th/0110146.

[6]  Á. Uranga,et al.  Dynamical SUSY breaking at meta-stable minima from D-branes at obstructed geometries , 2006, hep-th/0604136.

[7]  Alexander Postnikov,et al.  Total positivity, Grassmannians, and networks , 2006 .

[8]  D. Gaiotto,et al.  Gauge Theories Labelled by Three-Manifolds , 2011, 1108.4389.

[9]  From Sasaki-Einstein spaces to quivers via BPS geodesics: Lp,q|r , 2005, hep-th/0505206.

[10]  Yuji Tachikawa,et al.  Mirrors of 3d Sicilian theories , 2010, 1007.0992.

[11]  A. King,et al.  Dimer models and cluster categories of Grassmannians , 2013, 1309.6524.

[12]  Electric-magnetic duality in supersymmetric non-Abelian gauge theories , 1994, hep-th/9411149.

[13]  Rak-Kyeong Seong,et al.  Brane tilings and specular duality , 2012, 1206.2386.

[14]  Yu-tin Huang,et al.  ABJM amplitudes and the positive orthogonal Grassmannian , 2013, 1309.3252.

[15]  Dan Xie,et al.  The Positive orthogonal Grassmannian and loop amplitudes of ABJM , 2014 .

[16]  Preprint typeset in JHEP style- PAPER VERSION Freiburg-THEP-05/01 , 2005 .

[17]  Kelli Talaska,et al.  A Formula for Plücker Coordinates Associated with a Planar Network , 2008, 0801.4822.

[18]  S. Fomin,et al.  Cluster algebras I: Foundations , 2001, math/0104151.

[19]  A. Postnikov,et al.  Scattering Amplitudes and the Positive Grassmannian , 2012, 1212.5605.

[20]  Bernard Leclerc,et al.  Cluster algebras , 2014, Proceedings of the National Academy of Sciences.

[21]  The Dual superconformal theory for L**pqr manifolds , 2005, hep-th/0505220.

[22]  Brane dimers and quiver gauge theories , 2005, hep-th/0504110.

[23]  Gauge theories from toric geometry and brane tilings , 2005, hep-th/0505211.

[24]  D. Gaiotto.  Preprint Typeset in Jhep Style -hyper Version N = 2 Dualities , 2022 .

[25]  C. Beem,et al.  Four-dimensional SCFTs from M5-branes , 2012, 1203.0303.

[26]  M. Yamazaki,et al.  Network and Seiberg duality , 2012, 1207.0811.

[27]  S. Franco.  Cluster transformations from bipartite field theories. , 2013, 1301.0316.

[28]  Rak-Kyeong Seong,et al.  New directions in bipartite field theories , 2012, 1211.5139.

[29]  Shankhadeep Chakrabortty,et al.  w∞ 3-algebra , 2008 .

[30]  S. Franco.  Bipartite field theories: from D-brane probes to scattering amplitudes , 2012, 1207.0807.

[31]  David E Speyer,et al.  Matching polytopes, toric geometry, and the totally non-negative Grassmannian , 2009 .

[32]  Rak-Kyeong Seong,et al.  Double handled brane tilings , 2013, 1305.3607.

[33]  I. Bah,et al.  New N=1 Superconformal Field Theories In Four Dimensions , 2011, 1111.3402.

[34]  J. Maldacena,et al.  N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals , 2008, 0806.1218.

[35]  Kelli Talaska,et al.  Network Parameterizations for the Grassmannian , 2012, 1210.5433.

[36]  N. Arkani-Hamed,et al.  The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM , 2010, 1008.2958.

[37]  Nikolay Bobev,et al.  Two-dimensional SCFTs from wrapped branes and c-extremization , 2013, Journal of High Energy Physics.

[38]  Kristian D. Kennaway,et al.  Dimer models and toric diagrams , 2005, hep-th/0503149.

[39]  Mark Van Loon,et al.  Gauge theories, tessellations & Riemann surfaces , 2014, 1402.3846.

[40]  I. Bah,et al.  New $ \mathcal{N}=1 $ superconformal field theories in four dimensions , 2013 .

[41]  Á. Uranga,et al.  Bipartite field theories from D-branes , 2013, 1306.6331.

[42]  Yang-Hui He,et al.  Algorithmic algebraic geometry and flux vacua , 2006, hep-th/0606122.

[43]  Yang-Hui He,et al.  Dimer models from mirror symmetry and quivering amoebae , 2005, hep-th/0511287.

[44]  E. Witten,et al.  Direct proof of the tree-level scattering amplitude recursion relation in Yang-mills theory. , 2005, Physical Review Letters.

[45]  A. Amariti,et al.  Scattering amplitudes and toric geometry , 2013, 1305.5252.

[46]  S. Franco,et al.  An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals , 2004, hep-th/0411264.

[47]  Michael Joswig,et al.  polymake: a Framework for Analyzing Convex Polytopes , 2000 .

[48]  David E. Speyer,et al.  MATCHING POLYTOPES, TORIC GEOMETRY, AND THE NON-NEGATIVE PART OF THE GRASSMANNIAN , 2007, 0706.2501.

[49]  A. Mariotti,et al.  The geometry of on-shell diagrams , 2013, 1310.3820.

[50]  A. Vainshtein,et al.  Poisson geometry of directed networks in an annulus , 2008, 0901.0020.

[51]  Six-dimensional gauge theory on the chiral square , 2005, hep-ph/0506334.