IGLSM Conference - August 18,2020 "

-

3d Twists a Algebra .io Structures-

Based on world interaction al k .Costello

,D- Gareth

,N . Paquette , M .

Baltimore,T. Hilburn

,P

. Yoo.

A.Ballin

. U . Niu.N . Garner

Focus : 3rd N -

- 2 e N -

- 4 theories in flat 1123

Twist : choice of Q st. Q'-- O

3d N -

- 2 : unique (up to iso) IR'- Qzx IRE

In Los,- I contains 2E

, It

go's 3d N=4 :

generic nilp Q is fully topological : Im LQ,- I contains

+t 22- ZE , 2£SUK) # a Suede Q: t e it

'

Suez>⇐

hot- top or Qttt Ae QI:- -

top A- twist top B -foist

"

Q

Qa : Cest ¥;QB -Qt

I¥÷tgeaa¥l ops A = HaloedLrt

a fl shifted) Poisson vertex algebra(commutators)

v - 4 : have A

also AA , AB C- 2 shifted ) Poisson algebras

E. s. AA = Hooton.Cops)

- Hoon. ( Haacopsl) = Hien. CA)creepyexpect

3dN=2 flavor I - I 3

Exempt free chiral A = Gf olla , yeah,I

bos fern3d N-

- 4

free hyper A = etches, often ,

Ida, reeks) (huge)

Deformations : QB 4 = 20T Oaf = I

QB I = - 24 QAOT = - yT

hole sympe form or target ⇒

Aa - eGing)

AB - QL 4. OT ?- functions on T.cl - HI,z(The)

State - op correspondence : schematically A = Ha. ( Hills space on Df. D)

D-D

µfree chiral : stale -

op corresp says that

A = HE ( 0112-1 x RILED\ QQzD )-

cfcz) Gtz)

s't 46-3=442-3 for 2- €0= H 's ( QKZB ) namely as elders)

claim : correct this by using a denim d intersectioni.e

. imposing fete) -

- G'Ca)by introducing fermions St Al 3=4-4 '

corrected version :

,

A = ①Lefts , yes>

HI ( N . U2 Clkzb)A-twist Hdiz ( N°111 collab ) -

- Qvs

B - twit Hisle'S= AA - AB

5Gauge theory : A is not Cfnllg) known I

3dN=2 G. V expects A -- HE ( Gh.io?FEsesiYnirsfV- bundle

on Def. D , Lesley)-derived alg . geom3d N -

- 4 Aa = BFN construction if Coulomb branches= Hari ( same)

Ars e HE ( TV HG) slamsa

Recall : for 3dv=y A

Aa" "

ABMATU w3d MS 3d Ms

§Lineage Form a category (in any twist)÷

die Houle , l') - Hoa ( local ops atjuuetin)• factorization eat e in HT twist

lxoz l'

1 identity line (trivial line)

A -

- End :C A)\o C is graded by rotators€4 -

as Kees = Quantum K- theyshowing up in 3d f- 2 en s

'

In 3d N -- y e

r a

CA CB-braided ⑨ categories

§Babyex_ampk free chiral e = Cohl Geass)

3d N --2

+that thugsD=bdy cords for

"B-model on loop space of statant

contains : I = Gabayand vortex lines Vn =

zn¢µzy Mtk

End.CH) = functions on ①KHS

& deformations of QH7B into ①CGD( fermionic)

= EL GCH, 4th) = A

3dNL free hyperC -

- Con ( t.com)s w

ca = D -mod ( ECW) ④B = Cob LT- e)Rozanski, - written

§In 3d N-

- 4 , CA e CB Cats are now mostly understoodT T

C is not!

Bdy cords b AGI

←µ as bdy chiral algebras ← iutershg OPE's(modules for A)

C Es AGI -mod

jm3dN'- 4 A- or B twist 10,43 b. c . m blog VOA

( 2,2) b. e . as bdy algebra

hyper① ( 4th , open , et , I ) bullet

coin be. NN""

e ,¢e⇒ . us,# bdy fol 4To3n-

DDPTETQ ①Law. ETCH) § bulk QC4.FI

m bdy gets Tco) - tzz( 2,23 ND et etc" . It")

g- A hills all bdy modesDN XZ

B

CA -- D - mod ( Gaza) = pod⇒

Ctn ne k

Fu. . Ign [ Gu .oTm2 -

- Smtutho