The partition function of N=6 supersymmetric Chern-Simons-matter theory (known as ABJM theory) on S^3, as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super-matrix model is closely related to a matrix model describing topological Chern-Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS_4 x CP^3 and gives the correct N^{3/2} scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in CP^3. We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi-Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi-Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two 't Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi-Yau, and leads to an expansion around topological Chern-Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.
We construct the interaction terms between the worldvolume fields of multiple M2-branes and 3-form gauge field of 11-dimensional supergravity, in the context of ABJM theory. The obtained Wess-Zumino-type coupling is simultaneously invariant under the U$_{\textrm{L}}(N)\times$U$_{\textrm{R}}(N)$ non-Abelian gauge transformation of the ABJM theory and the Abelian gauge transformation of the 3-form field in 11-dimensional supergravity.
We compute the null cusp anomalous dimension of ABJM theory at strong coupling up to two-loop order. This is done by evaluating corrections to the corresponding superstring partition function, weighted by the $AdS_4\times \mathbb{CP}^3$ action in AdS light-cone gauge. We compare our result, where we use an anomalous shift in the $AdS_4$ radius, with the cusp anomaly of $\mathcal{N}=4$ SYM, and extract the two-loop contribution to the non-trivial integrable coupling $h(λ)$ of ABJM theory. It coincides with the strong coupling expansion of the exact expression for $ h(λ)$ recently conjectured by…
We study open strings on giant gravitons (D-branes on cycles) in the ABJM/$AdS_4\times \mathbb{CP}^3$ correspondence. We find that their energy spectrum has the same form as the one for closed strings, with a nontrivial function of the coupling, avoiding BMN scaling. A similar, Cuntz oscillator, Hamiltonian description for the string (operators at strong coupling) to the $AdS_5$ case is valid also in this case.
We introduce a new purely bosonic, $\frac{1}{6}$ BPS Wilson loop for ABJM theory on $S^3$ that couples scalar fields to a latitude at an angle $θ$ on $S^2\in\mathbb{C}P^3$. Through localization of this operator, we relate the expansion of the cusp anomalous dimension at small cusp angles to the logarithmic derivative of the ABJM Wilson loop. This defines, non-perturbatively in the 't Hooft coupling, the bremsstrahlung function $B(λ)$ describing in three dimensions the soft radiation of a $W$-boson undergoing a sudden change in trajectory. We compare our results for $B(λ)$ to the known weak/str…
We consider the Bremsstrahlung function associated to a 1/6-BPS Wilson loop in ABJM theory, with a cusp in the couplings to scalar fields. We non-trivially extend its recent four-loop computation at weak coupling to include non-planar corrections. We have recently proposed a conjecture relating this object to supersymmetric circular Wilson loops with multiple windings, which can be computed via localization. We find agreement between this proposal and the perturbative computation of the Bremsstrahlung function, including color sub-leading corrections. This supports the conjecture and hints at …
Using the Quantum Spectral Curve approach we compute exactly an observable (called slope function) in the planar ABJM theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semi-classical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders. By comparing the structure of our result with that of an exact localization-bas…
Using the matrix model which calculates the exact free energy of ABJM theory on S^3 we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the 't Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Further…
The free energy of ABJM theory has previously been computed in the strong and weak coupling limits. In this note, we report on results for the computation of the first non-vanishing quantum correction to the free energy, from the field theory side. The correction can be expressed in terms of a thermal mass for the scalar fields. This mass vanishes to 1-loop order, but there is a non-vanishing result to 2-loop order. Hence, the leading correction to the free energy is non-analytic in the 't Hooft coupling constant lambda. The reason is that the infrared divergences necessitate a resummation of …
When mass-deformed ABJM theory is considered on S(3), the partition function of the theory localises and is given by a matrix model. We solve this model at large-N in the decompactification limit, where the radius of the three-sphere is taken to infinity. In this limit, the theory exhibits a rich phase structure with an infinite number of third-order quantum phase transitions accumulating at strong coupling.
We study non-analytic behavior in the static charge susceptibility in finite density states of the ABJM theory using its holographic dual. Emphasis is placed on a particular state characterized by vanishing entropy density at zero temperature, and Fermi surface-like singularities in various fermionic correlation functions. The susceptibility exhibits branch points in the complex momentum plane, with a real part quantitatively very similar to the location of the Fermi surface singularities.
We find half-BPS vortex solitons, at both weak and strong coupling, in the N=6 supersymmetric mass deformation of ABJM theory with U(N) x U(N) gauge symmetry and Chern-Simons level k. The strong coupling gravity dual is obtained by performing a Z_k quotient of the N=8 supersymmetric eleven dimensional supergravity background of Lin, Lunin and Maldacena corresponding to the mass deformed M2-brane theory. At weak coupling, the BPS vortices preserving six supersymmetries are found in the Higgs vacuum of the theory where the gauge symmetry is broken to U(1) x U(1). The classical vortex solitons br…
We derive five-dimensional super Yang-Mills theory from mass-deformed ABJM theory by expanding about $S^2$ for large Chern-Simons level $K$. We obtain the Yang-Mills coupling constant $g_{YM}^2 = 4π^2 R/K$. If we consider $S^3/{\mb{Z}_K}$ as a fiber bundle over $S^2$ then $R/K$ is the circumference of the fiber. The value on the coupling constant agrees with what one gets by compactifying M five-brane on that fiber. For this computation we take $R,K\to \infty$ while keeping $R/K$ at a fixed finite value. We also study mass deformed star-three-product BLG theory at K=1 and $R\to \infty$. In tha…
The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. We find that all coefficients have maximal transcendentality. We then compute the four-loop wrapping correction for a scal…
In our previous work, the two-loop integrability of ABJM determinant like operator has been well established. In this paper, we push the integrability to all loop orders. The asymptotic Bethe ansatz equations for ABJM determinant like operator (open string attached on giant graviton) are obtained. In the derivation, the symmetries preserved by the bulk and the boundary played a crucial role. Taking the weak coupling limit and applying appropriate fermionic dualities, we obtained a different set of scalar sector Bethe equations with our previous results. When the "gauge" transformation on Bethe…
The localization technique allows us to compute the free energy of the U(N)_k x U(N)_{-k} Chern-Simons-matter theory dual to type IIA strings on AdS_4 x CP^3 from weak to strong 't Hooft coupling λ= N / k at finite N, as demonstrated by Drukker, Marino, and Putrov. In this note we study further the free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up all the 1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form -- the Airy function, Ai (k^{4/3}…
Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, a…
We study planar ABJM in a limit where one coupling is negligible compared to the other. We provide a recipe for exactly solving the expectation value of bosonic BPS Wilson loops on arbitrary smooth contours, or the leading divergence for cusped ones, using results from localization. As an application, we compute the exact (generalized) cusp anomalous dimension and Bremsstrahlung function and use it to determine the interpolating $h$-function. We finally prove a conjecture on the exact form of the dilatation operator in a closed sector, hinting at the integrability of this limit.
The phase structure of ABJM theory with mass $m$ deformation and non-vanishing Fayet-Iliopoulos (FI) parameter, $ζ$, is studied through the use of localisation on ${\mathbb S}^3$. The partition function of the theory then reduces to a matrix integral, which, in the large $N$ limit and at large sphere radius, is exactly computed by a saddle-point approximation. When the couplings are analytically continued to real values, the phase diagram of the model becomes immensely rich, with an infinite series of third-order phase transitions at vanishing FI-parameter. As the FI term is introduced, new ef…
Strong coupling dynamics of defect RG flows in ABJM
Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Dipartimento di Fisica, Università degli Studi di Milano–Bicocca and INFN, Sezione di Milano–Bicocca（米兰比可卡大学物理系及意大利国家核物理研究所米兰比可卡分部）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）
I consider three-point functions of twist-one operators in ABJM at weak coupling. I compute the structure constant of correlators involving one twist-one un-protected operator and two protected ones for a few finite values of the spin, up to two-loop order. As an application I enforce a limit on the gauge group ranks, in which I relate the structure constant for three chiral primary operators to the expectation value of a supersymmetric Wilson loop. Such a relation is then used to perform a successful five-loop test on the matrix model conjectured to describe the supersymmetric Wilson loop.
We analyse a light-like cusped Wilson loop in N=6 superconformal Chern-Simons theory at both weak and strong coupling in light-cone gauge. At the second order in the 't Hooft coupling $λ$ the correct cusp anomalous dimension $Γ_{\rm cusp}=-ϕ/ 2 λ^2$ is recovered through a deformation of the contour that takes both rays of the cusp slightly off of the light-cone. The strong coupling behaviour is addressed by means of the Bethe-Salpeter equation for ladders of tree-level gauge propagators and ladders of one-loop corrected gauge propagators. It turns out that, as might be expected, the contributi…
Assuming that the near horizon geometry of the black hole solution of the gravity dual to the ABJM model, in the presence of a coupling between the Weyl tensor and the field strength, is $AdS_{2}\times S^{2}$, we compute Sen's entropy function for this theory. By extremizing the entropy function we write a formula for the entropy of the black hole, and then we compute the same entropy using Wald's formula and show that the results are the same. In this way we generalize the calculation of black hole entropy to cases of curvature coupling to the field strength, including at first order, and we …
We consider general supersymmetric Wilson loops in ABJM model, i.e. Chern-Simons-matter theory in 2+1 dimensions with N=6 supersymmetry. They are so-called Zarembo-type: the Wilson loops of our interest have generic contours in spacetime, but the scalar field coupling is arranged accordingly so that there are unbroken supersymmetries. Based on the supermatrix formulation of Wilson loops by Drukker and Trancanelli, we construct explicitly 1/6-BPS Wilson loops and check that their expectation value is protected using perturbation up to two loops. We also study the dual string configuration in Ad…
As holographic description of BPS Wilson loops in ${\cal N}=3$ flavored ABJM theory with $N_f=k=1$, BPS M2-branes in $AdS_4\times N(1, 1)$ are studied in details. Two $1/3$-BPS membrane configurations are found. One of them is dual to the $1/3$-BPS Wilson loop of Gaiotto-Yin type. The regulated membrane action captures precisely the leading exponential behavior of the vacuum expectation values of $1/3$-BPS Wilson loops in the strong coupling limit, which was computed before using supersymmetric localization technique. Moreover, there is no BPS membrane with more supersymmetries in the backgrou…
In ABJ(M) theory a generalized cusp can be constructed out of the 1/6 BPS Wilson line by introducing an angle $φ$ in the spacial contour and/or an angle $θ$ in the internal R-symmetry space. The small angles limits of its anomalous dimension are controlled by corresponding Bremsstrahlung functions. In this note we compute the internal space $θ$-Bremsstrahlung function to four loops at weak coupling in the planar limit. Based on this result, we propose an all order conjecture for the $θ$-Bremsstrahlung function.
The matrix model of ABJM theory can be formulated in terms of a Fermi gas in an external potential. We show that, in this formalism, vevs of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern-Simons coupling, by using the WKB expansion. We present explicit results for the vevs of 1/6 and the 1/2 BPS Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obta…
We compute the 1-loop partition function for strings in $AdS_4\times\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level $k=2$, which in the large $N$ limit is holographically dual to weakly coupled M-theory on $AdS_4\times S^7/\mathbb{Z}_2$. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with…
We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the a…
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络温格物理研究中心）；Institut de Physique Théorique, Université Paris Saclay, CNRS（巴黎萨克雷大学理论物理研究所，法国国家科学研究中心）
We present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop operator in the corresponding ABJM matrix model. Using this formalism, we study the phase part of the ABJ partition function numerically and find a simple expression for it. We further compute a few exact values of the partition function at some coupling constants. Fitting these exact values against the expected form of the grand potential, we can determine the grand potential with exact coefficients. The res…
In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS Wilson loops on a latitude circular contour, so providing a new weak-strong interpolation tool. Intriguingly, the matrix model turns out to be a particular case of that computing torus knot invariants in $U(N_1|N_2)$ Chern-Simons theory. At weak coupling we check our proposal against a three-loop computation, performed for generic framing, winding number and representation. The matrix model is amenable of a Fermi gas formulation, which we use to systematically compute the strong coupling and genus expansions. For the f…
Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ_1,λ_2) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ_1,λ_2). We checked our conj…
Adapting a method recently proposed by C. Marboe and D. Volin for ${\cal N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the $sl(2)$-like sector of planar $\mathcal{N}$=6 super-Chern-Simons. The method relies on the Quantum Spectral Curve formulation of the problem and the expansion is written in terms of the interpolating function $h(λ)$, with coefficients expressible as combinations of Euler-Zagier sums with alternating signs. We present explicit results up to 12 loops (six nontrivial orders) for various twis…
The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of an ideal Fermi gas with a non-trivial, one-particle quantum Hamiltonian. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and N=3 quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections …
In 2008, Aharony, Bergman, Jafferis, and Maldacena (ABJM) discovered a three-dimensional Chern-Simons theory with N = 6 supersymmetry and conjectured that in a certain limit, this theory is dual to type IIA string theory on AdS4xCP3. Since then, a great deal of evidence has been accumulated which suggests that the ABJM theory is integrable in the planar limit. Integrability is a very useful property that allows many physical observables, such as anomalous dimensions and scattering amplitudes, to be computed efficiently. In the first half of this thesis, we will explain how to use integrabilty …
We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT$_1$ with SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS$_4 \times \mathbb{C}\textrm{P}^3$ ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-po…
There is a number of indications that scattering amplitudes in the Aharony-Bergman-Jafferis-Maldacena theory might have a dual description in terms of a holonomy of a supergauge connection on a null polygonal contour in a way analogous to the four-dimensional maximally supersymmetric Yang-Mills theory. However, so far its explicit implementations evaded a successful completion. The difficulty is intimately tied to the lack of the T-self-duality of the sigma model on the string side of the gauge/string correspondence. Unscathed by the last misfortune, we initiate with this study an application …
We consider twist-L operators in the planar N=6 superconformal Chern-Simons ABJM theory. Their anomalous dimension gamma_L^{CS}(N) is a function of the twist L, the spin N, and the dressed coupling of ABJM. We show that at next-to-leading order in the large spin expansion, this anomalous dimension is related to that of N=4 SYM twist operators by a simple scaling law.
We consider a special double scaling limit, recently introduced by two of the authors, combining weak coupling and large imaginary twist, for the $γ$-twisted $\mathcal{N}=4$ SYM theory. We also establish the analogous limit for ABJM theory. The resulting non-gauge chiral 4D and 3D theories of interacting scalars and fermions are integrable in the planar limit. In spite of the breakdown of conformality by double-trace interactions, most of the correlators for local operators of these theories are conformal, with non-trivial anomalous dimensions defined by specific, integrable Feynman diagrams. …
We construct the interaction terms between the world-volume fields of multiple M2-branes and the 3- and 6-form fields in the context of ABJM theory with U($N$)$\times$U($N$) gauge symmetry. A consistency check is made in the simplest case of a single M2-brane, i.e, our construction matches the known effective action of M2-brane coupled to antisymmetric 3-form field. We show that when dimensionally reduced, our couplings coincide with the effective action of D2-branes coupled to R-R 3- and 5-form fields in type IIA string theory. We also comment on the relation between a coupling with a specifi…
We tabulate various properties of the language of N=6 Chern-Simons Theory, in the sense of Polyakov. Specifically we enumerate and compute character formulas for all syllables of up to four letters, i.e. all irreducible representations of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We also present all tensor product decompositions for up to four singletons and list the (cyclically invariant) four-letter words, which correspond to single-trace operators of length four. As an application of these results we use the two-loop dilatation operator to compute the leading cor…
Recent progresses in the computation of quantum string corrections to holographic Wilson loops are extended to the case of strings in $AdS_{4}\times CP^{3}$. For this, the ratio of 1/2-BPS circular and 1/6-BPS latitude fermionic Wilson loops in ABJM is considered at strong coupling by studying the corresponding semiclassical string partition functions. Explicit evaluation of fluctuation determinants using phaseshifts and diffeomorphism invariant regulators leads to exact matching with the recent field theory proposal. Key to this computation is the choice of boundary conditions for massless fe…
We consider the four-point function of operators in the stress tensor multiplet of the $U(N)_k\times U(N)_{-k}$ ABJM theory, in the limit where $N$ is taken to infinity while $N/k^{5}$ is held fixed. In this limit, ABJM theory is holographically dual to type IIA string theory on $AdS_4\times \mathbb{CP}^3$ at finite string coupling $g_s \sim (N/k^5)^{1/4}$. While at leading order in $1/N$, the stress tensor multiplet four-point function can be computed from type IIA supergravity, in this work we focus on the first subleading correction, which comes from tree level Witten diagrams with an $R^4$…
We examine the string dual of the recently constructed $\mathcal{N}=6$ superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the $SU(2)\times SU(2)$ sector. We find a sigma-model limit in which the resulting sigma-model is two Landau-Lifshitz models added together. We consider a Penrose limit for which we can approach the $SU(2)\times SU(2)$ sector. Finally, we find a new Giant Magnon solution in the $SU(2)\times SU(2)$ sector corresponding to one magnon in each $SU(2)$. We put these results together to find the full magnon disp…
We calculate the non-abelian R-charges of BPS monopole operators in three-dimensional gauge theories with N=3 supersymmetry. This class of models includes ABJM theory, the proposed gauge theory dual of M-theory on AdS_4 x S^7/Z_k, as a special case. In the UV limit of the N=3 theories the Yang-Mills coupling becomes weak and the monopole operators are described by classical backgrounds. This allows us to find their SU(2)_R charges in a one-loop computation which by virtue of the non-renormalization of non-abelian R-charges yields the exact result for any value of the coupling. The spectrum of …
In $\mathcal N \geq 2$ superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol'nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a supermatrix inside a superalgebra. However, for particular choices of the param…
We compute the four-point amplitude in 3d N=8 SYM at two loops, by solving the three dimensional scalar doublebox in dimensional regularization. We compare it to the same result in the ABJM theory, to which maximal SYM should flow in the infrared at strong coupling. After proper rescalings, we find that the two amplitudes coincide in the Regge limit.
It was checked in paper [1] by comparing the moduli spaces and superconformal indices that two of the BLG theories $(SU(2)_{1}\times SU(2)_{-1})/{\mathbb Z}_2$ and $SU(2)_2\times SU(2)_{-2}$ are dual to $U(2)_1\times U(2)_{-1}$ and $U(2)_{2}\times U(2)_{-2}$ ABJM theories, correspondingly. In this paper we consider the BLG theories $SU(2)_1\times SU(2)_{-1}$ and $(SU(2)_2\times SU(2)_{-2})/{\mathbb Z}_2$. These theories were noted in [1] to be a tensor product of two interacting ${\mathcal N}=8$ SCFT's. In this paper we identify the SCFT's that occur in the product. For both theories one of th…
We study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using N=2 superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic N>=2 supersymmetric theories and find a vanishing result for N=6 ABJ(M) and N=8 BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known res…
Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS_4/CFT_3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the su(4) sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of N=6 superconformal Chern-Simons theory from osp(6|4) superconformal symmetry. For the osp(4|2) sector, we prove integrability through a Yangian construction. We argue that integrability extends to the full planar two-loop dilatation generator, confirming the applicability of the Beth…
We elaborate the Chern-Simons (CS) matrix models at large $N$. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't\,Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.
We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. $\textbf{Z}_k$, the gauge couplings of U$(1)$ gauge symmetries become weak in the limit of large $k$, as $g\to k^{-α}$ with $α$ a positive order 1 coefficient. The conjecture is based on black hole arguments combined with the Weak Gravity Conjecture (or the BPS bound in the supersymmetric setup), and the species bound. We provide explicit examples based on type IIB on AdS$_5\times \textbf{S}^5/\textbf{Z}_k$ orbifolds, and M-theory on AdS$_4\times\textbf{S}^7/\textbf{Z}_k$ ABJM orbifolds (and their type IIA reduct…
