Aharony-Bergman-Jafferis-Maldacena Research Articles

Duality cascades and parallelotopes

Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany–Witten transitions in brane configurations on a circle. In the setup of the Aharony–Bergman–Jafferis–Maldacena theory and its generalizations, from the physical requirement that duality cascades always end and the final destination depends only on the initial brane configuration, we propose that the fundamental domain of supersymmetric brane configurations in duality cascades can tile the whole parameter space of relative ranks by translations, hence is a parallelotope. We provide our arguments for the proposal.

Instantons in AdS$$_4$$ from (anti)membranes wrapping $$S^7$$ to Bose–Fermi duality in CFT$$_3$$’s

We present new SO(4)-invariant and non-supersymmetric instanton solutions for the conformally coupled m^2=-2 and massive m^2=+4 (pseudo)scalars arising from a consistent truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is a S^1 Hopf fibration on CP^3, and we consider backreaction. In fact, the bulk configurations associate with (anti)membranes wrapped around mixed internal (and external) directions, which in turn probe the Wick-rotated or skew-whiffed background, break all supersymmetries as well as parity invariance. From near the boundary behavior of the closed solution for the coupled bulk (pseudo)scalar, we get a marginal triple-trace deformation with mixed boundary condition (valid also for the bulk massless m^2=0 (pseudo)scalar, raised when considering the external space backreaction, with Dirichlet boundary condition) and as a result, the corresponding boundary effective potential is unbounded from below and causes an instability because of the Fubini-like instanton. Presenting dual effective actions, we see that the boundary solutions and counterparts realize in singlet sectors of three-dimensional U(N) and O(N) Chern--Simons-matter field theories. In particular, we use versions of massless and mass-deformed regular and critical boson and fermion models, find instantons and confirm state-operator AdS_4/CFT_3 correspondence and also Bose-Fermi duality at the level of the solutions. In addition, we discuss on relations of our setups with Vasiliev's Higher-Spin theories, deformations of the Aharony-Bergman-Jafferis-Maldacena model and other related studies.

Note on quantum periods and a TBA-like system

There is an interesting relation between the quantum periods on a certain limit of local P1×P1 Calabi-Yau space and a TBA (Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM (Aharony-Bergman-Jafferis-Maldacena) theory. We propose a one-parameter generalization of the relation. Furthermore, we derive the differential operators for quantum periods and the TBA-like equation in various limits of the generalized relation.

Quantum holographic entanglement entropy to all orders in 1/N expansion

Abstract We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the Wheeler–DeWitt equation, we compute quantum corrections to the holographic entanglement entropy for a circular entangling surface on the boundary three-sphere. Similarly to our previous work on the sphere partition function, the path integrals are dominated by a replica version of asymptotically anti-de Sitter conic geometries at saddle points. As expected from a general conformal field theory argument, the final result is minus the free energy on the three-sphere, which agrees with the logarithm of the Airy partition function for the Aharony–Bergman–Jafferis–Maldacena theory that sums up all perturbative $1/N$ corrections despite the absence of supersymmetries. The all-order holographic entanglement entropy cleanly splits into two parts, (1) the $1/N$-corrected Ryu–Takayanagi minimal surface area and (2) the bulk entanglement entropy across the minimal surface, as suggested in the earlier literature. It is explicitly shown that the former comes from the localized conical singularity of the replica geometries and the latter from the replication of the bulk volume.

BPS Wilson loops in mathcal{N} \u2265 2 superconformal Chern-Simons-matter theories

In mathcal{N} ≥ 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 super-matrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in mathcal{N} = 4 orbifold ABJM theory. In the particular case of mathcal{N} = 2 orbifold ABJM theory we identify the gravity duals of a subset of operators. We investigate the cohomological equivalence of fermionic and bosonic BPS Wilson loops at quantum level by studying their expectation values, and find strong evidence that the cohomological equivalence holds quantum mechanically, at framing one. Finally, we discuss a stronger formulation of the cohomological equivalence, which implies non-trivial identities for correlation functions of composite operators in the defect CFT defined on the Wilson contour and allows to make novel predictions on the corresponding unknown integrals that call for a confirmation.

Towards an M5-brane model I: A 6d superconformal field theory

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang–Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2, 0)-theory.

Color-kinematic duality in ABJM theory without amplitude relations

We explicitly show that the Bern–Carrasco–Johansson color-kinematic duality holds at tree level through at least eight points in Aharony–Bergman–Jafferis–Maldacena theory with gauge group [Formula: see text]. At six points we give the explicit form of numerators in terms of amplitudes, displaying the generalized gauge freedom that leads to amplitude relations. However, at eight points no amplitude relations follow from the duality, so the diagram numerators are fixed unique functions of partial amplitudes. We provide the explicit amplitude-numerator decomposition and the numerator relations for eight-point amplitudes.

Non-topological Vortex Configurations in the ABJM Model

In this paper we study the existence of vortex-type solutions for a system of self-dual equations deduced from the mass-deformed Aharony--Bergman--Jafferis--Maldacena (ABJM) model. The governing equations, derived by Mohammed, Murugan, and Nastse under suitable ansatz involving fuzzy sphere matrices, have the new feature that they can support only non-topological vortex solutions. After transforming the self-dual equations into a nonlinear elliptic $2\times 2$ system we prove first an existence result by means of a perturbation argument based on a new and appropriate scaling for the solutions. Subsequently, we prove a more complete existence result by using a dynamical analysis together with a blow-up argument. In this way we establish that, any positive energy level is attained by a 1-parameter family of vortex solutions which also correspond to (constraint) energy minimizers. In other words, we register the exceptional fact in a BPS-setting that, neither a "quantization" effect nor an energy gap is induced upon the system by the rigid "critical" coupling of the self-dual regime.

Construction of a massive ABJM theory without Higgs superfields

A massive Aharony-Bergman-Jafferis-Maldacena (ABJM) model in superspace is analysed by considering a Proca-type mass term into the most general Faddeev-Popov action in a covariant gauge. The presence of a mass term breaks the original BRST and anti-BRST invariance of the model. Further, the symmetry of the massive ABJM model is restored by extending the BRST and anti-BRST transformations. We show that the supergauge dependence of the generating functional for connected diagrams occurs in the presence of mass and ghost–anti-ghost condensates in the theory.

Exact results for Wilson loops in orbifold ABJM theory**Supported by NSFC (11222549, 11575202), K. C. Wong Education Foundation and Youth Innovation Promotion Association of CAS (2011016)

We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d = 3 mathcal = 4 super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition function of the mathcal = 4 orbifold ABJM theory has been computed previously in the literature. In this paper, we re-derive it using a slightly different method. We calculate the vacuum expectation values of the circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2 BPS Wilson loops in arbitrary representations. We use both the saddle point approach and Fermi gas approach. The results for Wilson loops are in accord with the available gravity results.

Construction and classification of novel BPS Wilson loops in quiver Chern–Simons-matter theories

In this paper we construct and classify novel Drukker–Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in N=2,3 quiver superconformal Chern–Simons-matter theories, Aharony–Bergman–Jafferis–Maldacena (ABJM) theory, and N=4 orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto–Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and N=4 orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are Q-exact with Q being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically.

Large N behavior of mass deformed ABJM theory

In this paper, using the localization technique we analyze the large N limit of the mass deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory on the three sphere with a finite mass parameter and finite Chern-Simons levels. We find two different solutions of the saddle point equations in the large N limit. With these solutions we compute the free energy and find that there is a first order phase transition. Our results may predict a phase transition in the dual gravity theory.

BPS Wilson loops in Minkowski spacetime and Euclidean space

We give evidence that spacelike BPS Wilson loops do not exist in Minkowski spacetime. We show that spacelike Wilson loops in Minkowski spacetime cannot preserve any supersymmetries, in $$d = 4$$ $$\mathcal N = 4$$ super Yang–Mills theory, $$d = 3$$ $$\mathcal N = 2$$ super Chern–Simons-matter theory, and $$d = 3$$ $$\mathcal N = 6$$ Aharony–Bergman–Jafferis–Maldacena theory. We not only show this using infinite straight lines and circles as examples, but also we give proofs for general curves. We attribute this to the conflicts of the reality conditions of the spinors. However, spacelike Wilson loops do exist in Euclidean space. There are both BPS Wilson loops along infinite straight lines and circular BPS Wilson loops. This is because the reality conditions of the spinors are lost after Wick rotation. The result is reasonable in view of the AdS/CFT correspondence.

Integrable amplitude deformations forN=4super Yang-Mills and ABJM theory

We study Yangian-invariant deformations of scattering amplitudes in 4d N=4 supersymmetric Yang-Mills theory and 3d N=6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Grassmannian integral for 4d N=4 super Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Grassmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.

A note on instanton effects in ABJM theory

We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local P^1*P^1 Calabi-Yau geometry. In the ABJM setting the problem is formulated by an integral equation, and is somewhat different from the one formulated directly in terms of the Calabi-Yau geometry and studied in our earlier paper. We use the similar method in our earlier paper to determine the non-perturbative contributions to the quantum phase volume in the ABJM case from the Bohr-Sommerfeld quantization condition. As in our earlier paper, the non-perturbative contributions contain higher order smooth corrections beyond those required by singularity cancellations with the perturbative contributions proposed by Kallen and Marino. Our results imply possible new contributions to the grand potential of the ABJM matrix model.

Marginal fluctuations as instantons on M2/D2-branes

We introduce some (anti-) M/D-branes through turning on the corresponding field strengths of the 11- and 10-dimensional supergravity theories over \(\hbox {AdS}_4 \times M^{7|6}\) spaces, where we use \(S^7/Z_k\) and \(CP^3\) for the internal spaces. Indeed, when we add M2/D2-branes on the same directions with the near horizon branes of the Aharony–Bergman–Jafferis–Maldacena model, all symmetries and supersymmetries are preserved trivially. In this case, we obtain a localized object just in the horizon. This normalizable bulk massless scalar mode is a singlet of \(SO(8)\) and \(SU(4) \times U(1)\), and it agrees with a marginal boundary operator of the conformal dimension of \(\Delta _+=3\). However, after performing a special conformal transformation, we see that the solution is localized in the Euclideanized \(\hbox {AdS}_4\) space and is attributable to the included anti-M2/D2-branes, which are also necessary to ensure that there is no back-reaction. The resultant theory now breaks all \({\mathcal {N}}=8,6\) supersymmetries to \({\mathcal {N}}=0\), while the other symmetries are so preserved. The dual boundary operator is then set up from the skew-whiffing of the representations \(\mathbf 8 _s\) and \(\mathbf 8 _v\) for the supercharges and scalars, respectively, while the fermions remain fixed in \(\mathbf 8 _c\) of the original theory. Besides, we also address another alternate bulk to boundary matching procedure through turning on one of the gauge fields of the full \(U(N)_k \times U(N)_{-k}\) gauge group along the same lines with a similar situation to the one faced in the AdS\(_5\)/CFT\(_4\) correspondence. The latter approach covers the difficulty already faced with in the bulk–boundary matching procedure for \(k=1,2\) as well.

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

The matrix model of the Aharony-Bergman-Jafferis-Maldacena theory can be formulated in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show that, in this formalism, vacuum expectation values (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 Wentzel- Kramer-Brillouin expansion.We present explicit results for the vevs of 1/6 and the 1/2 Bogomolnyi- Prasad-Sommerfield Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the ’t Hooft expansion.

Multiple Vortices in the Aharony–Bergman–Jafferis–Maldacena Model

Vortices in non-Abelian gauge field theory play important roles in confinement mechanism and are governed by systems of nonlinear elliptic equations of complicated structures. In this paper, we present a series of existence and uniqueness theorems for multiple vortex solutions of the BPS vortex equations, arising in the dual-layered Chern–Simons field theory developed by Aharony, Bergman, Jafferis, and Maldacena, over \({\mathbb{R}^2}\) and on a doubly periodic domain. In the full-plane setting, we show that the solution realizing a prescribed distribution of vortices exists and is unique. In the compact setting, we show that a solution realizing n prescribed vortices exists over a doubly periodic domain \({\Omega}\) if and only if the condition $$n < \frac{\lambda |\Omega|}{2 \pi}$$holds, where \({\lambda >0 }\) is the Higgs coupling constant. In this case, if a solution exists, it must be unique. Our methods are based on calculus of variations.

M-Theory in the Gaugeon Formalism

In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in superspace formalism. We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism. We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.

Classification of BPS objects in $ \mathcal{N} = 6 $ Chern-Simons matter theory

We investigate BPS conditions preserving n/12 (n = 1,...,6) supersymmetries in the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. The BPS equations are classified in terms of the number of preserved supercharges and remaining subgroups of the SU(4)_R symmetry. We study structures of a map between projection conditions for the supercharges in eleven dimensions and those in the ABJM model. The BPS configurations in the ABJM model can be interpreted as known BPS objects in eleven-dimensional Mtheory,such as intersecting M2, M5-branes, M-waves, KK-monopoles and M9-branes. We also show that these BPS conditions reduce to those in N = 8 super Yang-Mills theory via the standard D2-reduction procedure in a consistent way with the M-theory interpretation of the BPS conditions.