Supersymmetric Chern-Simons Matter Theories Research Articles

Monopole operators and symmetry enhancement in ABJM theory revisited

We construct monopole operators for 3D Yang-Mills matter theories and Chern-Simons matter theories in canonical formalism. In this framework, monopole operators, although they are disorder operators, could be written in terms of the fundamental fields of the theory, and thus could be treated in the same way as the ordinary operators. We study the properties of the constructed monopole operators. In Chern-Simons matter theories, monopole operators transform as the local operators with the classical conformal dimension 0 under the action of the dilation and are also covariantly constant. In supersymmetric Chern-Simons matter theories like the ABJM model, monopole operators commute with all of the supercharges, and thus are SUSY invariant. The ABJM model with level $k=1,2$ is expected to have enhanced $SO(8)$ R symmetry due to the existence of the conserved extra R-symmetry currents ${j}_{\ensuremath{\mu}}^{AB}$ involving monopoles. With the explicit form of the monopole operators given, we prove the current conservation equation ${\ensuremath{\partial}}^{\ensuremath{\mu}}{j}_{\ensuremath{\mu}}^{AB}=0$ using the equations of motion. We also compute the extra $\mathcal{N}=2$ supercharges, derive the extra $\mathcal{N}=2$ SUSY transformation rules, and verify the closure of the $\mathcal{N}=8$ supersymmetry.

Localization of three-dimensional $\mathcal{N}=2$ supersymmetric theories on $S^1 \times D^2$

Abstract We study three-dimensional $\mathcal{N}=2$ supersymmetric Chern—Simons matter theories on the direct product of a circle and a two-dimensional hemisphere ($S^1 \times {D^2}$) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of the three-dimensional superpotential term and the Chern—Simons term and show inflows of the bulk—boundary anomalies. We find that the boundary conditions induce two-dimensional $\mathcal{N}=(0,2)$-type supersymmetry on the boundary torus. We also study the relation between the three-dimensional—two-dimensional coupled partition function of our model and three-dimensional holomorphic blocks.

Topologically twisted index in the ’t Hooft limit and the dual AdS4 black hole entropy

We study the topologically twisted index of $\mathcal{N}=6$ supersymmetric Chern-Simons matter theory with $U(N)_k \times U(N)_{-k}$ gauge group in the 't Hooft limit, that is, for $N, k \, \to \infty$ with $\lambda=N/k$ fixed. In the regime where $\lambda$ is fixed and large we find an analytical expression for the leading order term of the index. The leading term of the index matches precisely the Bekenstein-Hawking entropy of the dual asymptotically AdS$_4$ magnetically charged black holes embedded in IIA supergrvity on AdS$_4\times \mathbb{CP}^3$, after a standard Legendre transformation. We numerically explore the genus expansion of the topologically twisteed index beyond the leading order, focusing on the genus one contribution, that is, $N^0$. We find qualitative agreement with the topological expansion of the free energy on $S^3$ at genus one. Our logarithmic in $\lambda$ term constitutes a prediction for the one-loop effective action on the IIA supergravity side.

Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

Resurgence and Lefschetz thimble in three-dimensional $\mathcal{N}=2$ supersymmetric Chern–Simons matter theories

We study a certain class of supersymmetric (SUSY) observables in 3d $\mathcal{N}=2$ SUSY Chern-Simons (CS) matter theories and investigate how their exact results are related to the perturbative series with respect to coupling constants given by inverse CS levels. We show that the observables have nontrivial resurgent structures by expressing the exact results as a full transseries consisting of perturbative and non-perturbative parts. As real mass parameters are varied, we encounter Stokes phenomena at an infinite number of points, where the perturbative series becomes non-Borel-summable due to singularities on the positive real axis of the Borel plane. We also investigate the Stokes phenomena when the phase of the coupling constant is varied. For these cases, we find that the Borel ambiguities in the perturbative sector are canceled by those in nonperturbative sectors and end up with an unambiguous result which agrees with the exact result even on the Stokes lines. We also decompose the Coulomb branch localization formula, which is an integral representation for the exact results, into Lefschetz thimble contributions and study how they are related to the resurgent transseries. We interpret the non-perturbative effects appearing in the transseries as contributions of complexified SUSY solutions which formally satisfy the SUSY conditions but are not on the original path integral contour.

How to resum perturbative series in 3dN=2Chern-Simons matter theories

Continuing the work arXiv:1603.06207, we study perturbative series in general 3d $\mathcal{N}=2$ supersymmetric Chern-Simons matter theory with $U(1)_R$ symmetry, which is given by a power series expansion of inverse Chern-Simons levels. We find that the perturbative series are usually non-Borel summable along positive real axis for various observables. Alternatively we prove that the perturbative series are always Borel summable along negative (positive) imaginary axis for positive (negative) Chern-Simons levels. It turns out that the Borel resummations along this direction are the same as exact results and therefore correct ways of resumming the perturbative series.

Brane resolution through fibration

We consider p-branes with one or more circular directions fibered over the transverse space. The fibration, in conjunction with the transverse space having a blown-up cycle, enables these p-brane solutions to be completely regular. Some such circularly-wrapped D3-brane solutions describe flows from SU(N)^3 N=2 theory, F_0 theory, as well as an infinite family of superconformal quiver gauge theories, down to three-dimensional field theories. We discuss the operators that are turned on away from the UV fixed points. Similarly, there are wrapped M2-brane solutions which describe smooth flows from known three-dimensional supersymmetric Chern-Simons matter theories, such as ABJM theory. We also consider p-brane solutions on gravitational instantons, and discuss various ways in which U-duality can be applied to yield other non-singular solutions.

New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes

We provide evidence for a duality between color and kinematics in three-dimensional supersymmetric Chern-Simons matter theories. We show that the six-point amplitude in the maximally supersymmetric N=8 theory can be arranged so that the kinematic factors satisfy the fundamental identity of three-algebras. We further show that the four- and six-point N=8 amplitudes can be squared into the amplitudes of N=16 three-dimensional supergravity, thus providing evidence for a hidden three-algebra structure in the dynamics of the supergravity.

Brane Effective Actions, Kappa-Symmetry and Applications.

This is a review on brane effective actions, their symmetries and some of their applications. Its first part covers the Green-Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects: the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry to achieve manifest spacetime covariance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds.Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as Bogomol’nyi-Prasad-Sommerfield (BPS) states carrying (topological) charges in the supersymmetry algebra and the connection between supersymmetry and Hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approximations to infer about the non-trivial dynamics of strongly-coupled gauge theories using the anti de Sitter/conformal field theory (AdS/CFT) correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description.Its final part briefly discusses effective actions for N D-branes and M2-branes. This includes both Super-Yang-Mills theories, their higher-order corrections and partial results in covariantising these couplings to curved backgrounds, and the more recent supersymmetric Chern-Simons matter theories describing M2-branes using field theory, brane constructions and 3-algebra considerations.

Index computation for 3d Chern-Simons matter theory: test of Seiberg-like duality

We work out the superconformal index for N=2 supersymmetric Chern-Simons matter theories exhibiting Seiberg-like dualities proposed by Giveon and Kutasov. We consider $U(N)/Sp(2N)/O(N)$ gauge theories of QCD type and find the perfect agreements for proposed dual pairs.

From correlators to Wilson loops in Chern-Simons matter theories

We study n-point correlation functions for chiral primary operators in three dimensional supersymmetric Chern-Simons matter theories. Our analysis is carried on in \( \mathcal{N} = 2 \) superspace and covers \( \mathcal{N} = 2,3 \) supersymmetric CFT’s, the \( \mathcal{N} = 6 \) ABJM and the \( \mathcal{N} = 8 \) BLG models. In the limit where the positions of adjacent operators become light-like, we find that the one-loop n-point correlator divided by its tree level expression coincides with a light-like n-polygon Wilson loop. Remarkably, the result can be simply expressed as a linear combination of five dimensional two-mass easy boxes. We manage to evaluate the integrals analytically and find a vanishing result, in agreement with previous findings for Wilson loops.

Spontaneous breaking of superconformal invariance in [formula omitted] supersymmetric Chern–Simons-matter theories in the large N limit

In this work we study the spontaneous breaking of superconformal and gauge invariances in the Abelian N = 1 , 2 three-dimensional supersymmetric Chern–Simons-matter (SCSM) theories in a large N flavor limit. We compute the Kählerian effective superpotential at subleading order in 1 / N and show that the Coleman–Weinberg mechanism is responsible for the dynamical generation of a mass scale in the N = 1 model. This effect appears due to two-loop diagrams that are logarithmic divergent. We also show that the Coleman–Weinberg mechanism fails when we lift from the N = 1 to the N = 2 SCSM model.

Infrared stability of $ \mathcal{N} = 2 $ Chern-Simons matter theories

According to the AdS4/CFT3 correspondence, N=2 supersymmetric Chern-Simons matter theories should have a stable fixed point in the infrared. In order to support this prediction we study RG flows of two-level Chern-Simons matter theories with/without flavors induced by the most general marginal superpotential compatible with N=2 supersymmetry. At two loops we determine the complete spectrum of fixed points and study their IR stability. Our analysis covers a large class of models including perturbations of the ABJM/ABJ theories with and without flavors, N=2,3 theories with different CS levels corresponding to turning on a Romans mass and beta-deformations. In all cases we find curves (or surfaces) of fixed points which are globally IR stable but locally unstable in the following sense: The system has only one direction of stability which in the ABJM case coincides with the maximal global symmetry preserving perturbation, whereas along any other direction it flows to a different fixed point on the surface. The question of conformal invariance vs. finiteness is also addressed: While in general vanishing beta-functions imply two-loop finiteness, we find a particular set of flavored theories where this is no longer true.

Rotating membranes in AdS 4 × M 1,1,1

Motivated by the recent progress on gravity duals of supersymmetric Chern-Simons matter theories, we consider classical membrane solutions in AdS_4 x M^{1,1,1}. In particular, we present several types of exact solutions rotating in the Sasaki-Einstein 7-manifold whose isometry is SU(3)xSU(2)xU(1). We analyze the limiting behavior of macroscopic membranes and discuss how one can identify the dual operators and the implications of our result on their conformal dimensions.

Notes on supersymmetry enhancement of ABJM theory

We study the supersymmetry enhancement of ABJM theory. Starting from a ${\cal N}=2$ supersymmetric Chern-Simons matter theory with gauge group U(2)$\times$U(2) which is a truncated version of the ABJM theory, we find by using the monopole operator that there is additional ${\cal N}=2$ supersymmetry related to the gauge group. We show this additional supersymmetry can combine with ${\cal N}=6$ supersymmetry of the original ABJM theory to an enhanced ${\cal N}=8$ SUSY with gauge group U(2)$\times$U(2) in the case $k=1,2$. We also discuss the supersymmetry enhancement of the ABJM theory with U($N$)$\times$U($N$) gauge group and find a condition which should be satisfied by the monopole operator.

Interacting SUSY-singlet matter in non-relativistic Chern–Simons theory

We construct an example of supersymmetric Chern–Simons-matter theory with a matter field transforming as a singlet representation of the supersymmetry algebra, where the bosonic and fermionic degrees of freedom do not match. This is obtained as a non-relativistic limit of the Chern–Simons-matter theory in 1+2 dimensions, where the particle and anti-particle coexist. We also study the index to investigate the mismatch of bosonic and fermionic degrees of freedom.