Dualities and correspondences

[blefloch]

• S-duality in 4d N=2
• Seiberg duality in 4d N=1, generalizations by Kutasov-Schwimmer (one adjoint), Brodie (two adjoints), Intriligator-Pouliot (symplectic), Argyres-Intriligator-Leigh-Strassler (two adjoints, no quark), duality cascade by Klebanov, and many by Intriligator-Leigh-Strassler
• 3d Aharony duality, Giveon-Kutasov,
• 2d Hori-Tong U(k), Hori Sp&SO, Kutasov-Lin (0,2), Gomis-LeFloch (2,2) with adjoint
• 3d mirror symmetry
• 2d mirror symmetry
• toric duality
• Kramers–Wannier duality in 2d Ising model
• boson/fermion in 2d CFT
• AdS/CFT correspondence
• AGT correspondence
• gauge/vortex duality
• 3d Chern-Simons level-rank duality

[blefloch]

3d dualities from 4d dualities

• Aharony Razamat Seiberg Willett original paper and for orthogonal groups
• Amariti Csáki, Martone Rey-Le Lorier From S-confinement to 3D Chiral Theories: Dressing the Monopoles

[blefloch]

http://arxiv.org/abs/hep-th/9910250 (get 4d N=1 dualities from 4d N=2 or N=4)

[blefloch]

String theory dualities: (see, e.g. http://arxiv.org/pdf/hep-th/9804208)

• Orbifold of IIB gives IIA
• Orientifold of IIB gives I
• S-duality of IIB string theory (32 susy)
• T-duality exchanging IIA and IIB wrapped on a circle R->\alpha'/R (32 susy)
• heterotic string on a 4-torus and Type IIA string on a K_3 surface (16 susy)
• heterotic string on a 2-torus and F-theory on a K_3 surface (16 susy)
• M-theory on a circle giving IIA
• F-theory on a 2-torus giving IIB

[blefloch]

http://arxiv.org/abs/1103.5700