An Introduction to Quantum Sheaf Cohomology - Physics - Virginia ...

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Example, cont’d ∫ ∫ ∏ 〈O 1 · · · O n 〉 = d 2 φ i P 4 i Limits: 1) λ → 0 dχ i dχ ı dχ p dχ p O 1 · · · O n · exp (−λ 2 |s| 2 − λχ i χ p D i s − λχ p χ ı D ı s − R ippk χ i χ p χ p χ k) Exponential reduces to purely curvature terms; bring down enough factors to each up χ p zero modes. Equiv to, inserting Euler class. 2) λ → ∞ Localizes on {s = 0} ⊂ P 4 Equivalent results, either way.
Renormalization (semi)group flow Constructs a series of theories that are approximations to the previous ones, valid at longer and longer distance scales. The effect is much like starting with a picture and then standing further and further away from it, to get successive approximations; final result might look very different from start. Problem: cannot follow it explicitly.
Page 1 and 2: An Introduction to Quantum Sheaf Co
Page 3 and 4: First, recall ordinary mirror symme
Page 5 and 6: (0,2) mirror symmetry Instead of ex
Page 7 and 8: (0,2) mirror symmetry A few highlig
Page 9 and 10: Aside on lingo: The worldsheet theo
Page 11 and 12: The A/2, B/2 models: * (0,2) analog
Page 13 and 14: A/2 model g ij ∂φ i ∂φ j + ih
Page 15 and 16: A model classical correlation funct
Page 17 and 18: A model -- worldsheet instantons Mo
Page 19 and 20: A/2 model -- worldsheet instantons
Page 21 and 22: 1st, review linear sigma model (LSM
Page 23 and 24: What about induced sheaves F → M
Page 25 and 26: Corresponding to O(k) is a rk k `un
Page 27 and 28: There is also a trivial extension o
Page 29 and 30: Quantum cohomology ... is an OPE ri
Page 31 and 32: Briefly, one computes quantum (shea
Page 33 and 34: (cont’d) Briefly, the (long exact
Page 35 and 36: (cont’d) Summary: The correlation
Page 37 and 38: More generally, for ``linear’’
Page 39 and 40: So far: * outlined A/2, B/2 models
Page 41 and 42: LG B model: The states of the theor
Page 43 and 44: To A twist, need a U(1) isometry on
Page 45 and 46: A twistable example: LG A model: LG
Page 47 and 48: LG A model, cont’d 〈O 1 · ·
Page 49: Example, cont’d Q · In the A twi
Page 53 and 54: Furthermore, RG preserves TFT’s.
Page 55 and 56: So far we’ve outlined (2,2) Landa
Page 57 and 58: Pseudo-topological twists: * If E a
Page 59 and 60: Adams-Basu-Sethi Example: Correspon
Page 61 and 62: One can also compute elliptic gener
Page 63 and 64: (cont’d) Perform A/2 twist. If re
Page 65 and 66: Most general case: LG model on with
Page 67 and 68: Example: NLSM on {G = 0} ⊂ W P 4
Page 69: Strings-Math 2011 A new biennial co

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