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We calculate the \\( 𝓢 \\){<}{/}{s}pan>-multiplets for two-dimensional Euclidean \\( 𝓝 \\){<}{/}{s}pan> = (0, 2) and \\( 𝓝 \\){<}{/}{s}pan> = (2, 2) superconformal field theories under the T \\( T̅ \\){<}{/}{s}pan> deformation at leading order of perturbation theory in the deformation coupling. Then, from these \\( 𝓝 \\){<}{/}{s}pan> = (0, 2) deformed multiplets, we calculate two- and three-point correlators. We show the \\( 𝓝 \\){<}{/}{s}pan> = (0, 2) chiral ring’s elements do not flow under the T \\( T̅ \\){<}{/}{s}pan> deformation. Specializing to integrable supersymmetric seed theories, such as \\( 𝓝 \\){<}{/}{s}pan> = (2, 2) Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer’s folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers’ equation. Finally, we show that several indices independent of D-term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the T \\( T̅ \\){<}{/}{s}pan> deformation.

Abstract We develop a manifest supertwistor space formalism for three dimensional N = 1 , 2 , 3 , 4 𝓝=1,2,3,4 superconformal field theories. This formalism simultaneously makes manifest the supersymmetry, conformal invariance and conservation. We solve two and three point correlators of (half) integer spin conserved supercurrents using the graded supergroup generators. Apart from the superconformal generators, we find that the superhelicity operators are necessary to fix their functional form in this setup. The superhelicity operators can be recast into first order Euler equations which besides the standard rational solutions, also admit weak solutions that are distributional in nature. They play an important role in the case of three point functions, where the supercorrelator takes the form of a product of delta functions. Interestingly, we find that these supercorrelators are extremely simple, elegant and uniform for all spins and for all N ≤ 4 𝓝≤ 4 , which resemble the non supersymmetric correlators where the twistors are replaced with appropriately defined supertwistors.

A bstract We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.

A bstract We propose a manifestly supersymmetric generalization of the solvable T T ¯ deformation of two-dimensional field theories. For theories with (1 , 1) and (0 , 1) supersymmetry, the deformation is defined by adding a term to the superspace Lagrangian built from a superfield containing the supercurrent. We prove that the energy levels of the resulting deformed theory are determined exactly in terms of those of the undeformed theory. This supersymmetric deformation extends to higher dimensions, where we conjecture that it might provide a higher-dimensional analogue of T T ¯ , producing supersymmetric Dirac or Dirac-Born-Infeld actions in special cases.

A bstract We investigate the “ T T ¯ ” deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the T T ¯ deforming operator can be constructed as a super-symmetric descendant. Here we focus on N = 1 0 and N = 1 1 supersymmetry. As an example, we analyse in detail the T T ¯ deformation of a free N = 1 0 supersymmetric action. We also argue that the link between T T ¯ and string theory can be extended to su-perstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the T T ¯ deformation of a free theory of eight N = 1 1 scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of T T ¯ deformations that have recently been discussed in the literature.

A bstract This paper focuses on the analysis of 4 d N = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of 1 2 -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4 d N = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4 d N = 4 superconformal theories with a line defect, 3 d N = 4 superconformal theories with no defect, and OSP(4 ∗ |4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions.

Abstract We compute the superconformal partial waves of the four-point correlator 〈JJJJ〉, in which the external operator J is the superconformal primary of the 4D N$$ \\mathcal{N} $$= 2 stress-tensor multiplet J$$ \\mathcal{J} $$. We develop the superembedding formalism for the superconformal field theories (SCFTs) with extended supersymmetry. In N$$ \\mathcal{N} $$= 2 SCFTs, the three- point functions JJO$$ \\left\\langle \\mathcal{JJO}\\right\\rangle $$with general multiplet O$$ \\mathcal{O} $$contain two independent nilpotent superconformal invariants and new superconformal tensor structures, which can be nicely constructed from variables in superembedding space, and the three-point functions can be written in compact forms. We compute the superconformal partial waves corresponding to the exchange of long multiplets using supershadow approach. The results are consistent with the non-trivial constraints by decomposing the N$$ \\mathcal{N} $$= 2 superconformal blocks into N$$ \\mathcal{N} $$= 1 superconformal blocks. Our results provide the necessary ingredient to study the fascinating 4D N$$ \\mathcal{N} $$= 2 SCFTs using conformal bootstrap.

A bstract We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT 1 with SU(1 , 1 | 3) super- conformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS 4 × ℂP 3 ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-point correlators of its components in terms of a single function of the one-dimensional cross-ratio. Such function is highly constrained by crossing and internal consistency, allowing us to use an analytical bootstrap approach to find the first subleading correction at strong coupling. Finally, we use AdS/CFT to compute the same four-point functions through tree-level AdS 2 Witten diagrams, producing a result that is perfectly consistent with the bootstrap solution.

A bstract We highlight the need for global completion of the field content in the M5-brane sigma-model analogous to Dirac’s charge/flux quantization, and we point out that the superspace Bianchi identities on the worldvolume and on its ambient supergravity background constrain the M5’s flux-quantization law to be in a non-abelian cohomology theory rationally equivalent to a twisted form of co-Homotopy. In order to clearly bring out this subtle point we give a streamlined re-derivation of the worldvolume 3-flux via M5 “super-embeddings”. Finally, assuming the flux-quantization law to actually be in co-Homotopy (“Hypothesis H”) we show how this implies Skyrmion-like solitons on general M5-worldvolumes and (abelian) anyonic solitons on the boundaries of “open M5-branes” in heterotic M-theory.

A bstract Flux quantization of the C-field in 11d supergravity is arguably necessary for the (UV-)completion of the theory, in that it determines the torsion charges carried by small numbers N ≪ ∞ of M-branes. However, hypotheses about C-field flux-quantization (“models of the C-field”) have previously been discussed only in the bosonic sector of 11d supergravity and ignoring the supergravity equations of motion. Here we highlight a duality-symmetric formulation of on-shell 11d supergravity on superspace, observe that this naturally lends itself to completion of the theory by flux quantization, and indeed that 11d super-spacetimes are put on-shell by carrying quantizable duality-symmetric super-C-field flux; the proof of which we present in detail.