Celestial dual superconformal symmetry, MHV amplitudes and differential equations

Celestial and momentum space amplitudes for massless particles are related to each other by a change of basis provided by the Mellin transform. Therefore properties of celestial amplitudes have counterparts in momentum space amplitudes and vice versa. In this paper, we study the celestial avatar of dual superconformal symmetry of $$ \mathcal{N} $$ N = 4 Yang-Mills theory. We also analyze various differential equations known to be satisfied by celestial n-point tree-level MHV amplitudes and identify their momentum space origins.

Three-point functions of higher-spin spinor current multiplets in $$ \mathcal{N} $$ = 1 superconformal theory

In this paper, we study the general form of three-point functions of conserved current multiplets Sα(k) = S(α1…αk) of arbitrary rank in four-dimensional $$ \mathcal{N} $$ N = 1 superconformal theory. We find that the correlation function of three such operators $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\beta \left(k+l\right)}\left({z}_2\right){\overline{S}}_{\dot{\gamma}(l)}\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S β k + l z 2 S ¯ γ ̇ l z 3 is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of k and l. In addition, we present the general structure of mixed correlators of the form $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right)L\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S α k z 2 L z 3 and $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right){J}_{\gamma \dot{\gamma}}\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S α k z 2 J γ γ ̇ z 3 , where L is the flavour current multiplet and $$ {J}_{\gamma \dot{\gamma}} $$ J γ γ ̇ is the supercurrent.

Correlation functions of spinor current multiplets in $$ \mathcal{N} $$ = 1 superconformal theory

We consider $$ \mathcal{N} $$ N = 1 superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet Sα and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with $$ \mathcal{N} $$ N = 2 supersymmetry and contains the current of the second supersymmetry. However, we do not assume $$ \mathcal{N} $$ N = 2 supersymmetry. We show that the three-point function of two spinor current multiplets and the $$ \mathcal{N} $$ N = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the $$ \mathcal{N} $$ N = 2 supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in $$ \mathcal{N} $$ N = 1 superconformal field theory does not necessarily imply $$ \mathcal{N} $$ N = 2 superconformal symmetry.

An $$ \mathcal{N} $$ = 1 Lagrangian for an $$ \mathcal{N} $$ = 3 SCFT

We propose that a certain 4d$$ \mathcal{N} $$ N = 1 SU(2) × SU(2) gauge theory flows in the IR to an $$ \mathcal{N} $$ N = 3 SCFT plus a single free chiral field. The specific $$ \mathcal{N} $$ N = 3 SCFT has rank 1 and a dimension three Coulomb branch operator. The flow is generically expected to land at the $$ \mathcal{N} $$ N = 3 SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from $$ \mathcal{N} $$ N = 3 superconformal symmetry, and use these to test our proposal. Finally, we discuss a generalization to another $$ \mathcal{N} $$ N = 1 model that we propose is related to a certain rank 3 $$ \mathcal{N} $$ N = 3 SCFT through the turning of certain marginal deformations.

Supersymmetric space-time symmetry breaking sources

We construct new families of deformed supersymmetric field theories which break space-time symmetries but preserve half of the original supersymmetry. We do this by writing deformations as couplings to background multiplets. In many cases it is important to use the off-shell representation as auxiliary fields of the non-dynamical fields must be turned on to preserve supersymmetry. We also consider backgrounds which preserve some superconformal symmetry, finding scale-invariant field profiles, as well as $$ \mathcal{N} $$ N = 2 theories on S3. We discuss how this is related to previous work on interface SCFTs and other holographic calculations.

Superconformal mechanics of AdS2 D-brane boundstates

We explicitly construct a family of $$ \mathcal{N} $$ N = 4 superconformal mechanics of dyonic particles, generalizing the work of Anninos et al. [1] to an arbitrary number of particles. These mechanics are obtained from a scaling limit of the effective Coulomb branch description of $$ \mathcal{N} $$ N = 4 quiver quantum mechanics describing D-branes in type II Calabi-Yau compactifications. In the supergravity description of these D-branes this limit changes the asymptotics to AdS2×S2×CY3. We exhibit the D(1, 2; 0) superconformal symmetry and conserved charges of the mechanics in detail. In addition we present an alternative formulation as a sigma model on a hyperkähler manifold with torsion.

Superconformal RG interfaces in holography

We construct gravitational solutions that holographically describe two different d = 4 SCFTs joined together at a co-dimension one, planar RG interface and preserving d = 3 superconformal symmetry. The RG interface joins $$ \mathcal{N} $$ N = 4 SYM theory on one side with the $$ \mathcal{N} $$ N = 1 Leigh-Strassler SCFT on the other. We construct a family of such solutions, which in general are associated with spatially dependent mass deformations on the $$ \mathcal{N} $$ N = 4 SYM side, but there is a particular solution for which these deformations vanish. We also construct a Janus solution with the Leigh-Strassler SCFT on either side of the interface. Gravitational solutions associated with superconformal interfaces involving ABJM theory and two d = 3 $$ \mathcal{N} $$ N = 1 SCFTs with G2 symmetry are also discussed and shown to have similar properties, but they also exhibit some new features.

Spatially modulated and supersymmetric mass deformations of $$ \mathcal{N} $$ = 4 SYM

We study mass deformations of $$ \mathcal{N} $$ N = 4, d = 4 SYM theory that are spatially modulated in one spatial dimension and preserve some residual supersymmetry. We focus on generalisations of $$ \mathcal{N} $$ N = 1∗ theories and show that it is also possible, for suitably chosen supersymmetric masses, to preserve d = 3 conformal symmetry associated with a co-dimension one interface. Holographic solutions can be constructed using D = 5 theories of gravity that arise from consistent truncations of SO(6) gauged supergravity and hence type IIB supergravity. For the mass deformations that preserve d = 3 superconformal symmetry we construct a rich set of Janus solutions of $$ \mathcal{N} $$ N = 4 SYM theory which have the same coupling constant on either side of the interface. Limiting classes of these solutions give rise to RG interface solutions with $$ \mathcal{N} $$ N = 4 SYM on one side of the interface and the Leigh-Strassler (LS) SCFT on the other, and also to a Janus solution for the LS theory. Another limiting solution is a new supersymmetric AdS4× S1× S5 solution of type IIB supergravity.

The superconformal equation

Crossing symmetry provides a powerful tool to access the non-perturbative dynamics of conformal and superconformal field theories. Here we develop the mathematical formalism that allows to construct the crossing equations for arbitrary four-point functions in theories with superconformal symmetry of type I, including all superconformal field the- ories in d = 4 dimensions. Our advance relies on a supergroup theoretic construction of tensor structures that generalizes an approach which was put forward in [1] for bosonic theories. When combined with our recent construction of the relevant superblocks, we are able to derive the crossing symmetry constraint in particular for four-point functions of arbitrary long multiplets in all 4-dimensional superconformal field theories.