Fractional M2-branes Research Articles

Tests of Seiberg-like dualities in three dimensions

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for mathcal{N} = 3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in mathcal{N} = 4 gauge theories realized by monopole operators.

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

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.

Wilson loops from D-branes in AdS 4×CP 3 with B NS holonomy

We study Wilson loops in N=6 superconformal Chern-Simons theory with gauge group $U(M) \times \bar{U(N)}$ that is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C4/Zk orbifold singularity. We give description of these Wilson loops in terms of macroscopic fundamental string and D6-branes in the dual AdS$_4\times$ CP$^3$ geometry with NS-NS B field turned on over CP$^1 \subset$ CP$^3$.

Finite-temperature fractional D2-branes and the deconfinement transition in 2+1 dimensions

The supergravity dual to N regular and M fractional D2-branes on the cone over \mathbb{CP}^3 has a naked singularity in the infrared. One can resolve this singularity and obtain a regular fractional D2-brane solution dual to a confining 2+1 dimensional N = 1 supersymmetric field theory. The confining vacuum of this theory is described by the solution of Cvetic, Gibbons, Lu and Pope. In this paper, we explore the alternative possibility for resolving the singularity - the creation of a regular horizon. The black-hole solution we find corresponds to the deconfined phase of this dual gauge theory in three dimensions. This solution is derived in perturbation theory in the number of fractional branes. We argue that there is a first-order deconfinement transition. Connections to Chern--Simons matter theories, the ABJM proposal and fractional M2-branes are presented.

Chern-Simons Theories and Wrapped M-Branes in Their Gravity Duals

We investigate a class of N=4 quiver Chern-Simons theories and their gravity duals. We define the group of fractional D3-brane charges in a type IIB brane setup with taking account of D3-brane creation due to Hanany-Witten effect, and confirm that it agrees with the 3-cycle homology of the dual geometry, which describes the charges of fractional M2-branes, M5-branes wrapped on 3-cycles. The relation between the fractional brane charge and the torsion of the three-form potential field is partially established. We also discuss the duality between baryonic operators in the Chern-Simons theories and M5-branes wrapped on 5-cycles in the dual geometries. The degeneracy and the conformal dimension of the operators are reproduced on the gravity side. We also comment on the relation between wrapped M2-branes and monopole operators. The baryonic operators we consider are not gauge invariant. We argue that the gauge invariance cannot be imposed on all the operators corresponding to wrapped M-branes in AdS4/CFT3 correspondence.

Fractional M2-branes

We consider two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(N) × U(N). The first generalization is to = 6 superconformal U(M) × U(N) theories, and the second to = 5 superconformal O(2M) × USp(2N) and O(2M+1) × USp(2N) theories. These theories are conjectured to describe M2-branes probing C4/Zk in the unitary case, and C4/k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M−N| fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.

Integrable spin chain of superconformal U(M) × $\overline{\mathop{\rm U}(N)}$ Chern-Simons theory

N=6 superconformal Chern-Simons theory with gauge group U(M)xU(N)} is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C4/Zk orbifold singularity. We show that, much like its regular counterpart of M=N, the theory at planar limit have integrability structure in the conformal dimension spectrum of single trace operators. We first revisit the Yang-Baxter equation for a spin chain system associated with the single trace operators. We show that the integrability by itself does not preclude parity symmetry breaking. We construct two-parameter family of parity non-invariant, alternating spin chain Hamiltonian involving three-site interactions between 4 and 4* of SU(4). At weak `t Hooft coupling, we study the Chern-Simons theory perturbatively and calculate anomalous dimension of single trace operators up to two loops. The computation is essentially parallel to the regular case M=N. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation, but to the one preserving parity symmetry. We give several intuitive explanations why the parity symmetry breaking is not detected in the Chern-Simons spin chain Hamiltonian at perturbative level. We suggest that open spin chain, associated with open string excitations on giant gravitons or dibaryons, can detect discrete flat holonomy and hence parity symmetry breaking through boundary field.

New complete noncompact Spin(7) manifolds

We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S 4. Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S 4, our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L 2-normalisable harmonic 4-form for the A 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L 2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In Appendix A we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 − similar to B 8 .

Gravity duals of fractional branes in various dimensions

We derive type II supergravity solutions corresponding to space-filling regular and fractional $\mathrm{D}p$ branes on $(9\ensuremath{-}p)$-dimensional conical transverse spaces. Fractional $\mathrm{D}p$-branes are wrapped $\mathrm{D}(p+2)$-branes; therefore, our solutions exist only if the base of the cone has a non-vanishing Betti number ${b}_{2}.$ We also consider 11-dimensional SUGRA solutions corresponding to regular and fractional M2 branes on 8-dimensional cones whose base has a non-vanishing ${b}_{3}.$ (In this case a fractional M2-brane is an M5-brane wrapped over a 3-cycle.) We discuss the gauge theory intepretation of these solutions, as well as of the solutions constructed by Cveti\ifmmode \check{c}\else \v{c}\fi{} and co-workers.