Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions

By R. Dijkgraaf, Lotte Hollands, P. Sułkowski, C. Vafa. 2007

177 citations recorded by the source corpus.

We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/179bf7d7169ef536d18d2ff4847dfcfbb1ad8f0c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. C. Vafa
2. Sergei Gukov
3. Marcos Mariño
4. Tudor Dimofte
5. Pavel Putrov
6. E. Witten
7. Abhijit Gadde
8. R. Dijkgraaf

In Statistical and Nonlinear Physics

1. C. Vafa
2. Marcos Mariño
3. Sergei Gukov
4. R. Dijkgraaf
5. S. Cecotti
6. Tudor Dimofte
7. Andrew Neitzke
8. E. Witten

Citations in the corpus

• R-Twisting and 4d/2d Correspondences (2010, methodology): “Following [12] we now consider the circle rotation along the anti-diagonal circle in C × Cx as the 11-th dimension, replacing C × Cx R(3).”
• Fivebranes and 3-manifold homology (2016, background): “pfree chiral fermions ub(1)Np 1 . The relation between VW theory on A p 1 singularity and free fermions as well as the the physical interpretation of the embedding csu(p) N ˆ(bu(1) 1)Npwas studied in [45]. It was formally understood as a change from descrete to continous basis in [25]. All in all di”
• Vortex Counting and Lagrangian 3-Manifolds (2010, background): “This is expected from the description of a surface operator as a Lagrangian brane in the open BPS theory, since such a Lagrangian brane is well-known to have a dual description as a free fermion field [57–59].”
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems (2009, background): “Moreover, the Riemann surface is ‘quantum’ in the sense that on the x-z plane there is a non-commutativity [15,29,30] given by [x, z] = gs, where gs is the topological string coupling constant.”
• Fivebranes and 4-manifolds (2013, background): “ [M4(−•1 ···−•1 | {z } p )] (3.78) where the splitting of parameters x= (x⊥,xk) is such that x⊥ = ( Q ixi) 1/p. A version of this relation without shifts due to Freed-Witten anomaly was considered in [74,89]. In general, a gluing of the form M4(g(1)) ⊔...⊔M4(g(n)) ⊔M4(−•p1)⊔...⊔M4(−p•m) B M 4(g) (3.”