Karthik Inbasekar

Correlation functions of the higher-spin current operators in large N Chern-Simons theories are important to understand approximate higher-spin symmetries in these theories. Moreover, they also provide stronger checks for conjectured dualities in these theories. In this paper, we compute the two, three and four-point functions of the operators in the spin zero multiplet of $$ \mathcal{N} $$ N = 2 Supersymmetric vector matter Chern-Simons theory at large N to all orders of ’t Hooft coupling. While the two- and three-point functions are computed by solving the Schwinger-Dyson equation, this method becomes intractable for the computation of the four-point functions. Thereby, we use bootstrap method to evaluate four-point function of scalar operator $$ {J}_0^f=\overline{\psi}\psi $$ J 0 f = ψ ¯ ψ and $$ {J}_0^b=\overline{\phi}\phi . $$ J 0 b = ϕ ¯ ϕ . Interestingly, because $$ \left\langle {J}_0^f{J}_0^f{J}_0^b\right\rangle $$ J 0 f J 0 f J 0 b is a contact term, the four point function of $$ {J}_0^f $$ J 0 f operator resembles the corresponding correlation function in the free theory, up to overall coupling constant dependent factors and up to some ‘bulk AdS’ contact terms. On the other hand the $$ {J}_0^b $$ J 0 b four-point function receives an additional contribution compared to the free theory expression due to the $$ {J}_0^f $$ J 0 f exchange. We find that the double discontinuity of this single trace operator $$ {J}_0^f $$ J 0 f vanishes and hence it only contributes to AdS-contact term.

We study $$ \mathcal{N} $$ N = 3 supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of SU(N). In the ’t Hooft large N limit, we compute the exact 2 → 2 scattering amplitudes of the fundamental scalar superfields to all orders in the ’t Hooft coupling λ. Our computations are presented in $$ \mathcal{N} $$ N = 1 superspace and make significant use of the residual SO(2) _R symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact 2 → 2 scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the $$ \mathcal{N} $$ N = 3 theory in the planar limit is tree-level exact to all orders in the ’t Hooft coupling λ. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.

We study $\mathcal{N} = 3$ supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of $SU(N)$. In the 't Hooft large $N$ limit, we compute the exact $2 \to 2$ scattering amplitudes of the fundamental scalar superfields to all orders in the 't Hooft coupling $\lambda$. Our computations are presented in $\mathcal{N} = 1$ superspace and make significant use of the residual $SO(2)_R$ symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact $2 \to 2$ scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the $\mathcal{N} = 3$ theory in the planar limit is tree-level exact to all orders in the 't Hooft coupling $\lambda$. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.

The maximal extension of supersymmetric Chern-Simons theory coupled to fundamental matter has $\mathcal{N} = 3$ supersymmetry. In this short note, we provide the explicit form of the action for the mass-deformed $\mathcal{N} = 3$ supersymmetric $U(N)$ Chern-Simons-Matter theory. The theory admits a unique triplet mass deformation term consistent with supersymmetry. We explicitly construct the mass-deformed $\mathcal{N} = 3$ theory in $\mathcal{N} = 1$ superspace using a fundamental and an anti-fundamental superfield.

The maximal extension of supersymmetric Chern-Simons theory coupled to fundamental matter has $\mathcal{N}=3$ supersymmetry. In this short paper, we provide the explicit form of the action for the mass-deformed $\mathcal{N}=3$ supersymmetric $U(N)$ Chern-Simons-matter theory. The theory admits a unique triplet mass-deformation term consistent with supersymmetry. We explicitly construct the mass-deformed $\mathcal{N}=3$ theory in $\mathcal{N}=1$ superspace using a fundamental and an antifundamental superfield.

Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like ${\cal N}=4$ SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level $2\to 2$ scattering amplitude in the 3d ${\cal N}=2$ Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the 't Hooft large $N$ limit, the $2\to 2$ scattering amplitude in this theory has been shown to be tree-level exact in non-anyonic channels, while having only an overall multiplicative coupling dependent renormalisation in the anyonic channel. Therefore, the dual superconformal symmetry that we demonstrate in this paper is all loop exact. This is unlike the previously studied highly supersymmetric theories where dual superconformal symmetry is anomalous at loop levels. Furthermore, we reverse the argument to study the extent to which dual superconformal invariance fixes the scattering amplitude in an ${\cal N}=2$ supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the $2\to2$ amplitude, while the coupling constant dependence remain unfixed. Further, we use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling dependence of scattering amplitude.

Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like $$ \mathcal{N} $$ N = 4 SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level 2 → 2 scattering amplitude in the 3d $$ \mathcal{N} $$ N = 2 Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the ’t Hooft large N limit, the 2 → 2 scattering amplitude in this theory has been shown to be tree-level exact in non-anyonic channels, while having only an overall multiplicative coupling dependent renormalisation in the anyonic channel. Therefore, the dual superconformal symmetry that we demonstrate in this paper is all loop exact. This is unlike the previously studied highly supersymmetric theories where dual superconformal symmetry is anomalous at loop levels. Furthermore, we reverse the argument to study the extent to which dual superconformal invariance fixes the scattering amplitude in an $$ \mathcal{N} $$ N = 2 supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the 2 → 2 amplitude, while the coupling constant dependence remain unfixed. Further, we use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling dependence of scattering amplitude.

We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be used to compute all tree level scattering amplitudes in terms of $2\to 2$ scattering amplitude in $\mathrm{U}(N)$ $\mathcal{N}=2$ Chern-Simons (CS) theory coupled to matter in the fundamental representation. As a by-product, we also obtain a recursion relation for the CS theory coupled to regular fermions, even though in this case standard BCFW deformations do not have a good asymptotic behavior. Moreover, at large $N$, $2\to 2$ scattering can be computed exactly to all orders in ’t Hooft coupling as was done in earlier works by some of the authors. In particular, for $\mathcal{N}=2$ theory, it was shown that $2\to 2$ scattering is tree level exact to all orders except in the anyonic channel [K. Inbasekar et al., J. High Energy Phys. 10 (2015) 176], where it gets renormalized by a simple function of ’t Hooft coupling. This suggests that it may be possible to compute the all loop exact result for arbitrary higher-point scattering amplitudes at large $N$.

We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be used to compute all tree level scattering amplitudes in terms of $2\rightarrow2$ scattering amplitude in $U(N)$ ${\mathcal N}=2$ Chern-Simons (CS) theory coupled to matter in fundamental representation. As a byproduct, we also obtain a recursion relation for the CS theory coupled to regular fermions, even though in this case standard BCFW deformations do not have a good asymptotic behaviour. Moreover at large $N$, $2\rightarrow 2$ scattering can be computed exactly to all orders in 't Hooft coupling as was done in earlier works by some of the authors. In particular, for ${\mathcal N}=2$ theory, it was shown that $2\rightarrow 2$ scattering is tree level exact to all orders except in the anyonic channel arXiv:1505.06571, where it gets renormalized by a simple function of 't Hooft coupling. This suggests that it may be possible to compute the all loop exact result for arbitrary higher point scattering amplitudes at large $N$.

Bianchi attractors are near horizon geometries with homogeneous symmetries in spatial directions. We construct supersymmetric Bianchi attractors in $\mathcal{N}=2,d=4$, 5 gauged supergravity. In $d=4$, we consider gauged supergravity coupled to vector and hypermultiplets. In $d=5$, we consider gauged supergravity coupled to vector multiplets with a generic gauging of symmetries of the scalar manifold and the $U(1{)}_R$ gauging of the $R$-symmetry. Analyzing the gaugino conditions, we show that when the fermionic shifts do not vanish, there are no supersymmetric Bianchi attractors. This is analogous to the known condition that for maximally supersymmetric solutions, all of the fermionic shifts must vanish. When the central charge satisfies an extremization condition, some of the fermionic shifts vanish and supersymmetry requires that the symmetries of the scalar manifold are not gauged. This allows supersymmetric Bianchi attractors sourced by massless gauge fields and a cosmological constant. In five dimensions in the Bianchi I class, we show that the anisotropic ${\mathrm{AdS}}_3\times {\mathbb{R}}^2$ solution is $1/2$ BPS (Bogomol’nyi-Prasad-Sommerfield). We also construct a new class of $1/2$ BPS Bianchi III geometries labeled by the central charge. When the central charge takes a special value, the Bianchi III geometry reduces to the known ${\mathrm{AdS}}_3\times {\mathbb{H}}^2$ solution. For the Bianchi V and VII classes, the radial spinor breaks all of supersymmetry. We briefly discuss the conditions for possible massive supersymmetric Bianchi solutions by generalizing the matter content to include tensor, hypermultiplets, and a generic gauging on the $R$-symmetry.