ABJ(M) and Fractional M2's with Fractional M2 Charge

Recently Aharony, Bergman and Jafferis (ABJ) have argued that a 3d U(N+M)xU(N) Chern-Simons gauge theory at level (k,-k) may have a vacuum with N=6 supersymmetry only if M<k+1 and if a certain period of the B-field in a IIA background is quantized. We use a braneology argument to argue that N=3 supersymmetry may be preserved under the weaker condition that 2Nk>M(M-k)-1 with no restriction on the B-field. IIB brane cartoons and 11d supergravity solutions corresponding to N=3 vacua that do not preserve N=6 supersymmetry are argued to represent cascading gauge theories, generalizing the N=2 Seiberg duality conjectured by Giveon and Kutasov. While as usual the M2-brane charge runs as a result of the twisted Bianchi identity for *G_4, the M5-brane charge running relies on the fact that it wraps a torsion homology cycle.Comment: 16 pages, 3 eps figure

Resolving the M2-brane

We construct deformed, T^2 wrapped, rotating M2-branes on a resolved cone over Q^{1,1,1} and Q^{1,1,1}/Z_2, as well as on a product of two Eguchi-Hanson instantons. All worldvolume directions of these supersymmetric and regular solutions are fibred over the transverse space. These constitute gravity duals of D=3, N=2 gauge theories. In particular, the deformed M2-brane on a resolved cone over Q^{1,1,1} and the S^1 wrapped M2-brane on a resolved cone over Q^{1,1,1}/Z_2 provide explicit realizations of holographic renormalization group flows in M-theory for which both conformal and Lorentz symmetries are broken in the IR region and restored in the UV limit. These solutions can be dualized to supersymmetric type IIB pp-waves, which are rendered non-singular either by additional flux or a twisted time-like direction.Comment: Latex, 23 pages, references adde

M5 from M2

Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of three dimensional manifolds. We show that the model contains self-dual 2-form gauge fields in 6 dimensions, and the result may be interpreted as the M5-brane world-volume action.Comment: 15 pages, minor modificatio

M2-M5 blackfold funnels

We analyze the basic M2-M5 intersection in the supergravity regime using the blackfold approach. This approach allows us to recover the 1/4-BPS self-dual string soliton solution of Howe, Lambert and West as a three-funnel solution of an effective fivebrane worldvolume theory in a new regime, the regime of a large number of M2 and M5 branes. In addition, it allows us to discuss finite temperature effects for non-extremal self-dual string soliton solutions and wormhole solutions interpolating between stacks of M5 and anti-M5 branes. The purpose of this paper is to exhibit these solutions and their basic properties.Comment: 19 pages, 5 figures, harvmac; typo corrected in equation (3.19

Half-BPS M2-brane orbifolds

Smooth Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 and preserving at least half of the supersymmetry have been recently classified. Requiring that amount of supersymmetry forces X to be a spherical space form, whence isometric to the quotient of the round 7-sphere by a freely-acting finite subgroup of SO(8). The classification is given in terms of ADE subgroups of the quaternions embedded in SO(8) as the graph of an automorphism. In this paper we extend this classification by dropping the requirement that the background be smooth, so that X is now allowed to be an orbifold of the round 7-sphere. We find that if the background preserves more than half of the supersymmetry, then it is automatically smooth in accordance with the homogeneity conjecture, but that there are many half-BPS orbifolds, most of them new. The classification is now given in terms of pairs of ADE subgroups of quaternions fibred over the same finite group. We classify such subgroups and then describe the resulting orbifolds in terms of iterated quotients. In most cases the resulting orbifold can be described as a sequence of cyclic quotients.Comment: 51 pages; v3: substantial revision (20% longer): we had missed some cases, but the paper now includes a check of our results via comparison with extant classification of finite subgroups of SO(4

Phases of M2-brane Theories

We investigate different toric phases of 2+1 dimensional quiver gauge theories arising from M2-branes probing toric Calabi-Yau 4 folds. A brane tiling for each toric phase is presented. We apply the 'forward algorithm' to obtain the toric data of the mesonic moduli space of vacua and exhibit the equivalence between the vacua of different toric phases of a given singularity. The structures of the Master space, the mesonic moduli space, and the baryonic moduli space are examined in detail. We compute the Hilbert series and use them to verify the toric dualities between different phases. The Hilbert series, R-charges, and generators of the mesonic moduli space are matched between toric phases.Comment: 60 pages, 28 figures, 6 tables. v2: minor correction

Interpreting the M2-brane Action

The world-volume theory of multiple M2-branes proposed recently has a free scalar field. For large vev of this scalar field the world-volume action reduces to that of multiple D2-branes with Yang-Mills coupling proportional to the vev. We suggest that the correct interpretation of this scalar field is as the radial position of the M2-brane center of mass in a cylindrical polar coordinate system. Regarding the azimuthal angle as compact we can regard this as a set of coincident D2-branes in type IIA string theory with varying dilaton and metric. We find that the effective world-volume theory on the D2-branes has Yang-Mills coupling proportional to the radial coordinate; furthermore the radial coordinate satisfies free field equations of motion. This agrees with the corresponding results derived from the M2-brane world-volume theory.Comment: LaTeX file, 6 page

KK6 from M2 in ABJM

We study the BPS equations in ABJM theory furthermore. Besides the known funnel solutions which are proposed to describe M2-M5 systems we find a new kind solution. We analyze the properties therein and see that it can describe M2-KK6 (2D membranes with 6D Kaluza-Klein monopole) systems. Our solutions also reveal new vacua in the mass deformed ABJM theory. Contrast to the previous investigation in which the vacua are reducible, ours may be irreducible. We also discuss a possible interpretation of the new BPS solutions as a M2-2M5 system.Comment: Latex 17 pages, typos corrected, add a little more discussion about nM

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table