Eric Sharpe - Examples of homological projective duality in physics

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Interpretation? We’ve found a set of integers, that play the same role as GW inv’ts, but for a nc res’n. I don’t know of a notion of GW theory for nc res’ns, but there’s work on DT invt’s (see e.g. Szendroi, Nagao, Nakajima, Toda) Perhaps some version of GW/DT can be used to define a set of integers that ought to be GW inv’ts?
Summary: * physical realization of hpd (nc res’n of) CI quadrics branched double cover as phases of abelian GLSM, i.e. V // C * * detour through physics of gerbes * D-brane probes of nc res’ns * Briefly: analogues of GW invt’s for nc res’ns
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Examples of homological projective
Page 3 and 4:
What did hpd teach us? Prior to ~ 2
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Outline: * physical realization of
Page 7 and 8:
Prototype for the exotic GLSM’s I
Page 9 and 10:
GLSM for P 3 [2,2] (=T 2 ): Looks l
Page 11 and 12: All phases of GLSM’s can be descr
Page 13 and 14: The other phase is more exciting: V
Page 15 and 16: A more important subtlety is the fa
Page 17 and 18: General decomposition conjecture Co
Page 19 and 20: Quick consistency check: A sheaf on
Page 21 and 22: GLSM’s Let’s now return to our
Page 23 and 24: V// − C × : Double cover P 1 Ber
Page 25 and 26: Next simplest example: // + : LG on
Page 27 and 28: The next example in the pattern is
Page 29 and 30: Check that we are seeing K’s nonc
Page 31 and 32: Summary so far: CP 7 [2,2,2,2] This
Page 33 and 34: More examples: CI of 2 quadrics in
Page 35 and 36: D-brane probes of nc resolutions Le
Page 37 and 38: Our D-brane probes of this Landau-G
Page 39 and 40: When is a matrix factorization `poi
Page 41 and 42: We’re interested in Landau-Ginzbu
Page 43 and 44: Example: Family [C 2 /Z 2 ] x,y ×
Page 45 and 46: So far: When the LG model flows in
Page 47 and 48: Case of an nc resolution, cont’d:
Page 49 and 50: So far: * examples of hpd realizing
Page 51 and 52: Let’s work through this in more d
Page 53 and 54: As a warm-up, let’s outline the G
Page 55 and 56: P 7 [2,2,2,2], cont’d In principl
Page 57 and 58: P 7 [2,2,2,2], cont’d After norma
Page 59 and 60: Result for P 7 [2,2,2,2]: n N 1 512
Page 61: Applying the same method, Compare G
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Eric Sharpe - Examples of homological projective duality in physics

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