47,185 research outputs found
Feynman Rules for QCD in Space-Cone Gauge
We present the Lagrangian and Feynman rules for QCD written in space-cone
gauge and after eliminating unphysical degrees of freedom from the gluonic
sector. The main goal is to clarify and allow for straightforward application
of these Feynman rules. We comment on the connection between BCFW recursion
relations and space-cone gauge.Comment: 7 pages, typos corrected, diagrams and clarifying text adde
Lattice Properties of Oriented Exchange Graphs and Torsion Classes
The exchange graph of a 2-acyclic quiver is the graph of mutation-equivalent
quivers whose edges correspond to mutations. When the quiver admits a
nondegenerate Jacobi-finite potential, the exchange graph admits a natural
acyclic orientation called the oriented exchange graph, as shown by Br\"ustle
and Yang. The oriented exchange graph is isomorphic to the Hasse diagram of the
poset of functorially finite torsion classes of a certain finite dimensional
algebra. We prove that lattices of torsion classes are semidistributive
lattices, and we use this result to conclude that oriented exchange graphs with
finitely many elements are semidistributive lattices. Furthermore, if the
quiver is mutation-equivalent to a type A Dynkin quiver or is an oriented
cycle, then the oriented exchange graph is a lattice quotient of a lattice of
biclosed subcategories of modules over the cluster-tilted algebra, generalizing
Reading's Cambrian lattices in type A. We also apply our results to address a
conjecture of Br\"ustle, Dupont, and P\'erotin on the lengths of maximal green
sequences.Comment: Changes to abstract and introduction; in v3, minor changes
throughout, added Lemma 7.3; in v4, abstract slightly changed, final version;
in v5, Lemma 7.3 from v4 removed because of an error in its proof. We give a
new proof of Lemma 7.4, which cited Lemma 7.
- …