Nonperturbative Tests of Three-Dimensional Dualities

We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three-sphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal N = 2 gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of N = 8 super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit

Supersymmetry enhancement by monopole operators

We describe a method which allows one to study hidden symmetries in a large class of strongly coupled supersymmetric gauge theories in three dimensions. We apply this method to the ABJM theory and to the infrared limit of N=4 SQCD with adjoint and fundamental matter. We show that the U(N) ABJM model with Chern-Simons level k=1 or k=2 has hidden N=8 supersymmetry. Hidden supersymmetry is also shown to occur in N=4 d=3 SQCD with one fundamental and one adjoint hypermultiplet. The latter theory, as well as the U(N) ABJM theory at k=1, are shown to have a decoupled free sector. This provides evidence that both models are dual to the infrared limit of N=8 U(N) super-Yang-Mills theory.Comment: 29 pages, late

Flavor brane on the baryonic branch of moduli space

We study an extra flavor in the cascading SU((k+1)M)xSU(k M) gauge theory by adding probe D7-brane to the geometry. By finding a solution to the kappa-symmetry equation we establish that the D7-brane is mutually supersymmetric with the background everywhere on the baryonic branch of moduli space. We also discuss possible applications of this result.Comment: 15 pages; v2 typo corrected, references adde

New and old N=8 superconformal field theories in three dimensions

We show that an infinite family of N=6 d=3 superconformal Chern-Simons-matter theories has hidden N=8 superconformal symmetry and hidden parity on the quantum level. This family of theories is different from the one found by Aharony, Bergman, Jafferis and Maldacena, as well as from the theories constructed by Bagger and Lambert, and Gustavsson. We also test several conjectural dualities between BLG theories and ABJ theories by comparing superconformal indices of these theories.Comment: 16 pages, late

On The Inflaton Potential From Antibranes in Warped Throats

We compute the force between a stack of smeared antibranes at the bottom of a warped throat and a stack of smeared branes at some distance up the throat, both for anti-D3 branes and for anti-M2 branes. We perform this calculation in two ways: first, by treating the antibranes as probes in the background sourced by the branes and second, by treating the branes as probes in the candidate background sourced by the antibranes. These two very different calculations yield exactly the same expression for the force, for all values of the brane-antibrane separation. This indicates that the force between a brane and an antibrane is not screened in backgrounds where there is positive charge dissolved in flux, and gives a way to precisely compute the inflaton potential in certain string cosmology scenarios.Comment: 9 page

Duality between N=5 and N=6 Chern-Simons matter theory

We provide evidences for the duality between ${\cal N}=6$ $U(M)_{4} \times U(N)_{-4}$ Chern-Simons matter theory and ${\cal N}=5$ $O(\hat{M})_{2} \times USp(2\hat{N})_{-1}$ theory for a suitable $\hat{M},\hat{N}$ by working out the superconformal index, which shows perfect matching. For ${\cal N}=5$ theories, we show that supersymmetry is enhanced to ${\cal N}=6$ by explicitly constructing monopole operators filling in $SO(6)_R$ $R$-currents. Finally we work out the large $N$ index of $O(2N)_{2k} \times USp(2N)_{-k}$ and show that it exactly matches with the gravity index on $AdS_4 \times S^7/D_k$, which further provides additional evidence for the duality between the ${\cal N}=5$ and ${\cal N}=6$ theory for $k=1$Comment: 15 pages; references adde

Enhanced Supersymmetry of Nonrelativistic ABJM Theory

We study the supersymmetry enhancement of nonrelativistic limits of the ABJM theory for Chern-Simons level $k=1,2$. The special attention is paid to the nonrelativistic limit (known as `PAAP' case) containing both particles and antiparticles. Using supersymmetry transformations generated by the monopole operators, we find additional 2 kinematical, 2 dynamical, and 2 conformal supercharges for this case. Combining with the original 8 kinematical supercharges, the total number of supercharges becomes maximal: 14 supercharges, like in the well-known PPPP limit. We obtain the corresponding super Schr\"odinger algebra which appears to be isomorphic to the one of the PPPP case. We also discuss the role of monopole operators in supersymmetry enhancement and partial breaking of supersymmetry in nonrelativistic limit of the ABJM theory.Comment: 22 pages, references added, version to appear in JHE

Aspects of ABJM orbifolds with discrete torsion

We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order $m$ of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of $m$ in addition to the other effects that were found before in the literature. Therefore we got a $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian

Precision Spectroscopy and Higher Spin symmetry in the ABJM model

We revisit Kaluza-Klein compactification of 11-d supergravity on S^7/Z_k using group theory techniques that may find application in other flux vacua with internal coset spaces. Among the SO(2) neutral states, we identify marginal deformations and fields that couple to the recently discussed world-sheet instanton of Type IIA on CP^3. We also discuss charged states, dual to monopole operators, and the Z_k projection of the Osp(4|8) singleton and its tensor products. In particular, we show that the doubleton spectrum may account for N=6 higher spin symmetry enhancement in the limit of vanishing 't Hooft coupling in the boundary Chern-Simons theory.Comment: 44 page

Massive type IIA string theory cannot be strongly coupled

Understanding the strong coupling limit of massive type IIA string theory is a longstanding problem. We argue that perhaps this problem does not exist; namely, there may be no strongly coupled solutions of the massive theory. We show explicitly that massive type IIA string theory can never be strongly coupled in a weakly curved region of space-time. We illustrate our general claim with two classes of massive solutions in AdS4xCP3: one, previously known, with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive examples, as the rank N of the gauge group is increased, the dilaton initially increases in the same way as in the corresponding massless case; before it can reach the M-theory regime, however, it enters a second regime, in which the dilaton decreases even as N increases. In the N = 2 case, we find supersymmetry-preserving gauge-invariant monopole operators whose mass is independent of N. This predicts the existence of branes which stay light even when the dilaton decreases. We show that, on the gravity side, these states originate from D2-D0 bound states wrapping the vanishing two-cycle of a conifold singularity that develops at large N.Comment: 43 pages, 5 figures. v2: added reference