Eric Sharpe - Examples of homological projective duality in physics

Setup:
To study D-brane probes at the LG points,
we’ll RG flow the GLSM a little bit,
to build an `intermediate’ Landau-Ginzburg model.
(D-brane probes = certain matrix fact’ns in LG)
LG on
P n [2,2,..,2] (k intersections) is hpd to
Tot
with superpotential
(
O(−1/2) n+1
)
−→ P k−1
[2,2,···,2]
W = ∑ a
p a Q a (φ) = ∑ i,j
φ i A ij (p)φ j