90 research outputs found
Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics
We study BPS line defects in N=2 supersymmetric four-dimensional field
theories. We focus on theories of "quiver type," those for which the BPS
particle spectrum can be computed using quiver quantum mechanics. For a wide
class of models, the renormalization group flow between defects defined in the
ultraviolet and in the infrared is bijective. Using this fact, we propose a way
to compute the BPS Hilbert space of a defect defined in the ultraviolet, using
only infrared data. In some cases our proposal reduces to studying
representations of a "framed" quiver, with one extra node representing the
defect. In general, though, it is different. As applications, we derive a
formula for the discontinuities in the defect renormalization group map under
variations of moduli, and show that the operator product algebra of line
defects contains distinguished subalgebras with universal multiplication rules.
We illustrate our results in several explicit examples.Comment: 76 pages, 10 figures; v2: minor revisions, correction to Coulomb
branch calculation for defects in SU(2) SY
Hyperkahler Sigma Model and Field Theory on Gibbons-Hawking Spaces
We describe a novel deformation of the 3-dimensional sigma model with
hyperk\"ahler target, which arises naturally from the compactification of a
4-dimensional theory on a hyperk\"ahler circle bundle
(Gibbons-Hawking space). We derive the condition for which the deformed sigma
model preserves 4 out of the 8 supercharges. We also study the contribution
from a NUT center to the sigma model path integral, and find that supersymmetry
implies it is a holomorphic section of a certain holomorphic line bundle over
the hyperk\"ahler target. We study explicitly the case where the original
4-dimensional theory is pure super Yang-Mills, and show that the
contribution from a NUT center in this case is simply the Jacobi theta
function.Comment: 48 page
Spectral networks and Fenchel-Nielsen coordinates
We explain that spectral networks are a unifying framework that incorporates
both shear (Fock-Goncharov) and length-twist (Fenchel-Nielsen) coordinate
systems on moduli spaces of flat SL(2,C) connections, in the following sense.
Given a spectral network W on a punctured Riemann surface C, we explain the
process of "abelianization" which relates flat SL(2)-connections (with an
additional structure called "W-framing") to flat C*-connections on a covering.
For any W, abelianization gives a construction of a local Darboux coordinate
system on the moduli space of W-framed flat connections. There are two special
types of spectral network, combinatorially dual to ideal triangulations and
pants decompositions; these two types of network lead to Fock-Goncharov and
Fenchel-Nielsen coordinates respectively.Comment: 63 pages; v2: expository improvements, journal versio
Asymptotics of Hitchin's metric on the Hitchin section
We consider Hitchin's hyperk\"ahler metric on the moduli space
of degree zero -Higgs bundles over a compact
Riemann surface. It has been conjectured that, when one goes to infinity along
a generic ray in , converges to an explicit "semiflat" metric
, with an exponential rate of convergence. We show that this
is indeed the case for the restriction of to the tangent bundle of the
Hitchin section .Comment: 22 pages, 1 figure. v2: Minor revision
- …