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1. Bootstrapping M-theory orbifolds

   https://doi.org/10.1007/JHEP06(2024)001  

   Chester, Shai M; Pufu, Silviu S; Wang, Yifan; Yin, Xi (June 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We analyze correlation functions of SU(k) × SU(2)_Fflavor currents in a family of three-dimensional$$ \mathcal{N} $$ $N$ = 4 superconformal field theories, combining analytic bootstrap methods with input from supersymmetric localization. Via holographic duality, we extract gluon and graviton scattering amplitudes of M-theory on AdS₄×S⁷/ℤ_kwhich contains a ℂ²/ℤ_korbifold singularity. From these results, we derive aspects of the effective description of M-theory on the orbifold singularity beyond its leading low energy limit. We also determine a threshold correction to the holographic correlator from the combined contribution of two-loop gluon and tree-level bulk graviton exchange. 

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2. Large charge ’t Hooft limit of $$ \mathcal{N} $$ = 4 super-Yang-Mills

   https://doi.org/10.1007/JHEP02(2024)047  

   Caetano, João; Komatsu, Shota; Wang, Yifan (February 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> The planar integrability of$$ \mathcal{N} $$ $N$ = 4 super-Yang-Mills (SYM) is the cornerstone for numerous exact observables. We show that the large charge sector of the SU(2)$$ \mathcal{N} $$ $N$ = 4 SYM provides another interesting solvable corner which exhibits striking similarities despite being far from the planar limit. We study non-BPS operators obtained by small deformations of half-BPS operators withR-chargeJin the limitJ→ ∞ with$$ {\lambda}_J\equiv {g}_{\textrm{YM}}^2J/2 $$ ${\lambda }_J\equiv g_{\mathrm{YM}}^{2}J/2$ fixed. The dynamics in thislarge charge ’t Hooft limitis constrained by a centrally-extended$$ \mathfrak{psu} $$ $\mathrm{psu}$ (2|2)²symmetry that played a crucial role for the planar integrability. To the leading order in 1/J, the spectrum is fully fixed by this symmetry, manifesting the magnon dispersion relation familiar from the planar limit, while it is constrained up to a few constants at the next order. We also determine the structure constant of two large charge operators and the Konishi operator, revealing a rich structure interpolating between the perturbative series at weak coupling and the worldline instantons at strong coupling. In addition we compute heavy-heavy-light-light (HHLL) four-point functions of half-BPS operators in terms of resummed conformal integrals and recast them into an integral form reminiscent of the hexagon formalism in the planar limit. For general SU(N) gauge groups, we study integrated HHLL correlators by supersymmetric localization and identify a dual matrix model of sizeJ/2 that reproduces our large charge result atN= 2. Finally we discuss a relation to the physics on the Coulomb branch and explain how the dilaton Ward identity emerges from a limit of the conformal block expansion. We comment on generalizations including the large spin ’t Hooft limit, the combined largeN-largeJlimits, and applications to general$$ \mathcal{N} $$ $N$ = 2 superconformal field theories. 

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3. Topologically charged BPS microstates in AdS3/CFT2

   https://doi.org/10.1007/JHEP03(2025)069  

   Ardehali, Arash Arabi; Krishna, Hare (March 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> In the standard$$ \mathcal{N} $$ $N$ = (4, 4) AdS₃/CFT₂with sym^N(T⁴), as well as the$$ \mathcal{N} $$ $N$ = (2, 2) Datta-Eberhardt-Gaberdiel variant with sym^N(T⁴/ℤ₂), supersymmetric index techniques have not been applied so far to the CFT states with target-space momentum or winding. We clarify that the difficulty lies in a central extension of the SUSY algebra in the momentum and winding sectors, analogous to the central extension on the Coulomb branch of 4d$$ \mathcal{N} $$ $N$ = 2 gauge theories. We define modified helicity-trace indices tailored to the momentum and winding sectors, and use them for microstate counting of the corresponding bulk black holes. In the$$ \mathcal{N} $$ $N$ = (4, 4) case we reproduce the microstate matching of Larsen and Martinec. In the$$ \mathcal{N} $$ $N$ = (2, 2) case we resolve a previous mismatch with the Bekenstein-Hawking formula encountered in the topologically trivial sector by going to certain winding sectors. 

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4. Phase transitions at unusual values of θ

   https://doi.org/10.1007/JHEP12(2025)004  

   Csáki, Csaba; Kawano, Teruhiko; Murayama, Hitoshi; Telem, Ofri (December 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We calculate theθdependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is$$ \mathcal{N} $$ $N$ = 2 SU(2) gauge theory withN_F= 0, 1, 2, 3 flavors of fundamentals, explicitly broken to$$ \mathcal{N} $$ $N$ = 1 via an adjoint superpotential, and coupled to anomaly mediated supersymmetry breaking (AMSB). The hierarchym_AMSB≪μ_𝒩=1≪ Λ ensures the validity of our IR analysis. As expected from ordinary QCD, the vacuum energy is a function ofθwhich undergoes 1st order phase transitions between different vacua where the various dyons condense. ForN_F= 0 we find the expected phase transition atθ=π, while forN_F= 1, 2, 3 we find phase transitions at fractional values ofπ. 

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5. Extended JT supergravity and random matrix models: The power of the string equation

   https://doi.org/10.1007/JHEP03(2026)126  

   Johnson, Clifford V; Kolanowski, Maciej (March 2026, Journal of High Energy Physics)

   A<sc>bstract</sc> A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as$$ {\textrm{e}}^{S_0} $$ $e^{S_0}$ , whereS₀is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of$$ \mathcal{N}=2 $$ $N=2$ and (small)$$ \mathcal{N}=4 $$ $N=4$ JT supergravity, and then explore the new cases of spectra from$$ \mathcal{N}=3 $$ $N=3$ and large$$ \mathcal{N}=4 $$ $N=4$ JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions. 

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