Topological twistsof

non-Lagrangian theories

• Theories with non-freely generated Coulomb branch chiral rings

• N=3 theories

[P.Argyres, M.Lotito, Y.Lu, M.Martone]

• Argyres-Douglas theories

[O.Aharony, M.Evtikhiev][I.Garca-Etxebarria, D.Regalado]

[O.Aharony, Y.Tachikawa]:

[P.Argyres, M.Douglas][D.Xie]

:

=S x S index

Coulomb branch index

Topological1 3

[M.Dedushenko, S.G., P.Putrov]

4d theory

2d theory[M.Bershadsky, A.Johansen, V.Sadov, C. Vafa]

[J.Harvey, G.Moore, A.Strominger][A.Losev, N.Nekrasov, S.Shatashvili]

[J.Maldacena, C.Nunez][A.Kapustin, E.Witten]

:

S-folds

T-folds

Self-mirror

effective dilaton:

[C.Beem, M.Lemos, P.Liendo, L.Rastelli, B.C.van Rees]

4d N = 1UV

IR

4d N = 2

[A.Gadde, S. Razamat, B.Willett][K.Maruyoshi, J.Song]

:

4d N = 1UV

2d N = (0,2)

IR

4d N = 2

2d N = (2,2)

4d N = 1UV

2d N = (0,2)

adjoint SQCD

N = 1ffff

N = 1 adjoint

SQCD N = 0ffff

u

cf. [D.Kutasov, A.Parnachev, D.Sahakyan][K.Intriligator, B.Wecht]

:

4d N = 1UV

2d N = (0,2)

adjoint SQCD

SU(2) vector,

g+1 adjoint chirals, g adjoint Fermi,:

N = 1ffff

N = 1 adjoint

SQCD N = 0ffff

u

4d N = 1UV

2d N = (0,2) 2d N = (2,2)

The Witten index of 2d N = (2,2) theoryobtained from reduction of

Argyres-Douglas theory(A ,A )1 3

(A ,A )1 2

(A ,A )1 3

(A ,A )1 2

(A ,A )1 3

[L.Fredrickson, D.Pei, W.Yan, K.Ye]

x