Aharony-Bergman-Jafferis-Maldacena Theory Research Articles

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.

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.

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.

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.

Multitrace deformation of the Aharony-Bergman-Jafferis-Maldacena theory

Motivated by the study of big crunch singularities in asymptotically ${\mathrm{AdS}}_{4}$ space-times, we consider a marginal triple trace deformation of Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The deformation corresponds to adding a potential which is unbounded below. In a 't Hooft large $N$ limit, the beta function for the triple trace deformation vanishes, which is consistent with the near-boundary behavior of the bulk fields. At the next order in the $1/N$ expansion, the triple trace couplings exhibit nontrivial running, which we analyze explicitly in the limit of zero 't Hooft coupling, in which the model reduces to an $O(N)\ifmmode\times\else\texttimes\fi{}O(N)$ vector model with large $N$. In this limit, we establish the existence of a perturbative UV fixed point, and we comment on possible nonperturbative effects. We also show that the bulk analysis leading to big crunch singularities extends to the ${\mathbb{Z}}_{k}$ orbifold models dual to ABJM theory.

Vortex-type half-BPS solitons in Aharony-Bergman-Jafferis-Maldacena theory

We study the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory without and with mass deformation. It is shown that maximally supersymmetry preserving, D-term, and F-term mass deformations of single mass parameter are equivalent. We obtain vortex-type half-BPS equations and the corresponding energy bound. For the undeformed ABJM theory, the resulting half-BPS equation is the same as that in supersymmetric Yang-Mills theory and no finite energy regular BPS solution is found. For the mass-deformed ABJM theory, the half-BPS equations for U(2)xU(2) case reduce to the vortex equation in Maxwell-Higgs theory, which supports static regular multivortex solutions. In U(N)xU(N) case with N>2 the non-Abelian vortex equation of Yang-Mills-Higgs theory is obtained.

MULTIPLE D2-BRANE ACTION FROM M2-BRANES

We study the detailed derivation of the multiple D2-brane effective action from multiple M2-branes in the Bagger–Lambert–Gustavsson (BLG) theory and the Aharony–Bergman–Jafferis–Maldacena (ABJM) theory by employing the novel Higgs mechanism. We show explicitly that the high-order F3 and F4 terms are commutator terms, and conjecture that all the high-order terms are commutator terms. Because the commutator terms can be treated as the covariant derivative terms, these high-order terms do not contribute to the multiple D2-brane effective action. Inspired by the derivation of a single D2-brane from a M2-brane, we consider the curved M2-branes and introduce an auxiliary field. Integrating out the auxiliary field, we indeed obtain the correct high-order F4 terms in the D2-brane effective action from the BLG theory and the ABJM theory with SU(2) × SU(2) gauge symmetry, but we cannot obtain the correct high-order F4 terms from the ABJM theory with U(N) × U(N) and SU(N) × SU(N) gauge symmetries for N > 2. We also briefly comment on the (gauged) BF membrane theory.

Generalized conformal symmetry and recovery of [formula omitted] in multiple M2 and D2 branes

We investigate conformal symmetries of the Aharony–Bergman–Jafferis–Maldacena (ABJM) theory for multiple M2 branes and the Lorentzian Bagger–Lambert–Gustavsson (L-BLG) theory which can be obtained by taking a scaling limit k ( ≫ N ) → ∞ of the ABJM theory. The conformal symmetry is maintained in the L-BLG by considering general space–time varying solutions to the constraint equations. The dual geometry is reduced to d = 10 AdS 4 × CP 3 in the scaling limit and has the same conformal symmetry. The curvature radius R satisfies l p ( 11 ) ≪ l p ( 10 ) ≪ R ≪ l s ( l p ( d ) and l s are the d-dimensional Planck lengths and the string scale), and the theory is in a region where an α ′ expansion is not valid. We also study how the SO ( 8 ) covariance is recovered in the AdS 4 × CP 3 geometry by taking the scaling limit.