Is toric duality a Seiberg-like duality in (2 + 1)-d ?

Abstract

Abstract:We show that not all (2 + 1) dimensional toric phases are Seiberg-like duals. Particularly, we work out superconformal indices for the toric phases of Fanos C 3 , C 5 and B 2 . We find that the indices for the two toric phases of Fano B 2 do not match, which implies that they are not Seiberg-like duals. We also take the route of acting Seiberg-like duality transformation on toric quiver Chern-Simons theories to obtain dual quivers. We study two examples and show that Seiberg-like dual quivers are not always toric quivers.

Spin(7) duality for N $$ \mathcal{N} $$ = 1 CS-matter theories

“…Another well known duality for three dimensional field theories is the AdS 4 /CFT 3 correspondence [9][10][11] that relates Chern-Simons (CS) matter theories to M theory AdS 4 solutions. In this case it has been shown that there are different UV field theory descriptions of the IR theory living on M2 branes probing the same toric Calabi-Yau four dimensional cone CY 4 [6,[12][13][14][15]. This phenomenon has been named toric duality and it is the three dimensional extension of the previously discovered toric duality for the four dimensional field theories living on D3-branes probing Calabi-Yau three dimensional cones CY 3 [16][17][18][19].…”

Embedding and partial resolution of complex cones over Fano threefolds

“…Now we will discuss about the embedding of Fano P 3 inside Fano C 5 . It is interesting to note that Fano C 5 itself has two toric dual quiver gauge theories, known as phase-I and phase-II of Fano C 5 as shown in figure 3, which have been discussed in [37,47]. Both of these phases have the same toric data as that of Fano C 5 , but with different multiplicity of one of the point.…”