Type IIB construction of flavoured ABJ(M) and fractional M2 branes

TL;DR

This work presents a Type IIB brane construction for 3d flavoured ABJ(M) theories with YM terms, showing how IR fixed points correspond to M2 branes on toric CY_4 singularities and how different gauge ranks map to dual AdS_4×Y_7 backgrounds with torsion G-flux. By engineering quivers with fixed superpotentials and CS levels via fivebrane webs, the authors connect brane dynamics (including the s-rule and D3-brane creation) to dual M-theory data, reproducing known cases such as Q^{1,1,1} and Y^{1,2}(CP^2) and predicting torsion flux structures through H^4_{ ext{tor}}(Y_7,Z) with order n determined by brane creation. They analyze duality cascades, fractional M2 branes, and partial resolutions, showing how partial deformations in IIB correspond to RG flows between UV and IR fixed points and how torsion flux can extend along the flow. The paper also identifies smooth SE geometries forming one-parameter families whose torsion flux orders match the number of inequivalent SCFTs, and discusses caveats for singular Y_7 cases. Overall, the Type IIB perspective provides a concrete, controllable framework to study flavoured ABJ(M) theories, their RG flows, and the corresponding M-theory backgrounds, with implications for unHiggsing and broader CY_4 moduli spaces.

Abstract

We study type IIB brane configurations engineering 3d flavoured ABJ(M) theories with Yang-Mills kinetic terms, which flow to IR fixed points describing M2 branes at a class of toric Calabi-Yau fourfold singularities. The type IIB construction provides a bridge between M-theory geometry and field theory, and allows to identify the superconformal field theories with fixed quiver diagram, Chern-Simons levels and superpotential, differing by the ranks of the gauge groups, which we associate to dual AdS_4\timesY_7 backgrounds of M-theory without or with torsion G-fluxes sourced by fractional M2 branes in Y_7, when Y_7 is smooth. The analysis includes the Q^{1,1,1} and Y^{1,2}(CP^2) geometries. We also comment on duality cascades and on the interplay between torsion G-fluxes in M-theory and partial resolutions.

Figures (17)

• Figure 1: Type IIB brane configuration for the 3d KW theory. The two NS5 branes are depicted by (dashed) blue and red lines, the suspended D3 branes by the black dot. The $x^6$ circle is suppressed.
• Figure 2: Type IIB brane configuration, open strings and matter fields (4589 directions suppressed).
• Figure 3: Type IIB brane configuration for 3d KW with $F_1+F_2$ doubled vectorlike flavours.
• Figure 4: Quiver diagram of flavoured ABJM theories: circles are gauge groups, squares are flavour groups, arrows are chiral superfields in the fundamental representation of the tail and antifundamental representation of the head. CS levels are denoted in red.
• Figure 5: Web deformations (in the 37 plane) of the NS5-D5 system that leave massless favours, and corresponding spurionic VEVs. D3 branes intersect the fivebrane webs at the black dot.