Wall-crossing for vortex partition function and handsaw quiver varierty

Handsaw Quiver Varieties and Finite W -algebras

Following Braverman–Finkelberg–Feigin–Rybnikov (arXiv: 1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W -algebra of type A. This is a finite analog of the AGT conjecture on 4-dimensional supersymmetric Yang–Mills theory with surface operators. Our new observation is that the C-fixed point set of a handsaw quiver variety is...

Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

BPS Partition Functions for Quiver Gauge Theories: Counting Fermionic Operators

We discuss a general procedure to obtain 1/2 BPS partition functions for generic N = 1 quiver gauge theories. These functions count the gauge invariant operators (bosonic and fermionic), charged under all the global symmetries (mesonic and baryonic), in the chiral ring of a given quiver gauge theory. In particular we discuss the inclusion of the spinor degrees of freedom in the partition functi...

Vortex collisions: crossing or recombination?

We investigate the collision of two vortex lines moving with viscous dynamics and driven towards each other by an applied current. Using London theory in the approach phase we observe a nontrivial vortex conformation producing antiparallel segments; their attractive interaction triggers a violent collision. The collision region is analyzed using the time-dependent Ginzburg-Landau equation. Whil...

Wall Crossing and M-Theory

We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a CalabiYau 3-fold X. When X has no compact 4-cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in Mtheory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as ...