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1. Chern-Simons theory from M5-branes and calibrated M2-branes

   https://doi.org/10.1007/JHEP08(2019)165  

   Mezei, Márk; Pufu, Silviu S.; Wang, Yifan (August 2019, Journal of High Energy Physics)

   A bstract We study a sector of the 5d maximally supersymmetric Yang-Mills theory on S 5 consisting of 1 / 8-BPS Wilson loop operators contained within a great S 3 inside S 5 . We conjecture that these observables are described by a 3d Chern Simons theory on S 3 , analytically continued to a pure imaginary Chern-Simons level. Therefore, the expectation values of these 5d Wilson loops compute knot invariants. We verify this conjecture in the weakly-coupled regime from explicit Feynman diagram computations. At strong coupling, these Wilson loop operators lift to 1 / 8-BPS surface operators in the 6d (2 , 0) theory on S 1 × S 5 . Using AdS/CFT, we show that these surface operators are dual to M2-branes subject to certain calibration conditions required in order to preserve supersymmetry. We compute the renormalized action of a large class of calibrated M2-branes and obtain a perfect match with the field theory prediction. Finally, we present a derivation of the 3d Chern-Simons theory from 5d super-Yang-Mills theory using supersymmetric localization, modulo a subtle issue that we discuss. 

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2. Hidden U(N) symmetry behind $$ \mathcal{N} $$ = 1 superamplitudes

   https://doi.org/10.1007/JHEP11(2023)215  

   Delgado, Antonio; Martin, Adam; Wang, Runqing (November 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we develop a Young diagram approach to constructing higher dimensional operators formed from massless superfields and their superderivatives in$$ \mathcal{N} $$ $N$= 1 supersymmetry. These operators are in one-to-one correspondence with non-factorizable terms in on-shell superamplitudes, which can be studied with massless spinor helicity techniques. By relating all spin-helicity variables to certain representations under a hidden U(N) symmetry behind the theory, we show each non-factorizable superamplitude can be identified with a specific Young tableau. The desired tableau is picked out of a more general set of U(N) tensor products by enforcing the supersymmetric Ward identities. We then relate these Young tableaux to higher dimensional superfield operators and list the rules to read operators directly from Young tableau. Using this method, we present several illustrative examples. 

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3. Constructing operator basis in supersymmetry: a Hilbert series approach

   https://doi.org/10.1007/JHEP04(2023)097  

   Delgado, Antonio; Martin, Adam; Wang, Runqing (April 2023, Journal of High Energy Physics)

   A bstract In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give explicitly the form of the corrections that remove redundancies due to the equations of motion and integration by parts. In addition, we derive the maps between the correction spaces. This technique allows us to calculate the number of independent operators involving chiral and antichiral superfields to arbitrarily high mass dimension. Using this method, we give several illustrative examples. 

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4. Extended super BMS algebra of celestial CFT

   https://doi.org/10.1007/JHEP09(2020)198  

   Fotopoulos, Angelos; Stieberger, Stephan; Taylor, Tomasz R.; Zhu, Bin (September 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract We study two-dimensional celestial conformal field theory describing four- dimensional $$ \mathcal{N} $$ N =1 supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct fermionic conformal primary wave functions and show how they are related via supersymmetry to their bosonic partners. We use soft and collinear theorems of supersymmetric Einstein-Yang- Mills theory to derive the OPEs of the operators associated to massless particles. The bosonic and fermionic soft theorems are shown to form a sequence under supersymmetric Ward identities. In analogy with the energy momentum tensor, the supercurrents are shadow transforms of soft gravitino operators and generate an infinite-dimensional super- symmetry algebra. The algebra of $$ {\mathfrak{sbms}}_4 $$ sbms 4 generators agrees with the expectations based on earlier work on the asymptotic symmetry group of supergravity. We also show that the supertranslation operator can be written as a product of holomorphic and anti-holomorphic supercurrents. 

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5. Aspects of irregular punctures via holography

   https://doi.org/10.1007/JHEP11(2022)131  

   Bah, Ibrahima; Bonetti, Federico; Nardoni, Emily; Waddleton, Thomas (November 2022, Journal of High Energy Physics)

   A bstract We present new families of AdS 5 solutions in M-theory preserving 4d $$ \mathcal{N} $$ N = 2 supersymmetry. We perform a systematic analysis of holographic observables for these solutions, providing evidence for an interpretation in terms of 4d superconformal field theories (SCFTs) of Argyres-Douglas type, realized in class $$ \mathcal{S} $$ S via a sphere with one irregular, and one regular puncture. The gravity solutions exhibit internal M5-brane sources that correspond to the irregular puncture. For a family of solutions, we identify explicitly the class $$ \mathcal{S} $$ S puncture data and perform a detailed match, including Higgs branch operators. For other families we comment on proposed field theory duals, based on irregular punctures labeled by nested Young tableaux. 

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