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1. 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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2. $$ \mathcal{N} $$ = 2 JT supergravity and matrix models

   https://doi.org/10.1007/JHEP12(2023)003  

   Turiaci, Gustavo J.; Witten, Edward (December 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> Generalizing previous results for$$ \mathcal{N} $$ $N$= 0 and$$ \mathcal{N} $$ $N$= 1, we analyze$$ \mathcal{N} $$ $N$= 2 JT supergravity on asymptotically AdS₂spaces with arbitrary topology and show that this theory of gravity is dual, in a holographic sense, to a certain random matrix ensemble in which supermultiplets of differentR-charge are statistically independent and each is described by its own$$ \mathcal{N} $$ $N$= 2 random matrix ensemble. We also analyze the case with a time-reversal symmetry, either commuting or anticommuting with theR-charge. In order to compare supergravity to random matrix theory, we develop an$$ \mathcal{N} $$ $N$= 2 analog of the recursion relations for Weil-Petersson volumes originally discovered by Mirzakhani in the bosonic case. 

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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. Lower Bounds Against Sparse Symmetric Functions of ACC Circuits: Expanding the Reach of #SAT Algorithms

   https://doi.org/10.1007/s00224-022-10106-8  

   Vyas, Nikhil; Williams, R_Ryan (November 2022, Theory of Computing Systems)

   Abstract We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$ $\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[n^{{\left(\log n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$$\mathcal { C}$$ $C$, by showing that$$\mathcal { C}$$ $C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class$${\mathcal C}$$ $C$. Say that a symmetric Boolean functionf(x₁,…,x_n) issparseif it outputs 1 onO(1) values of$${\sum }_{i} x_{i}$$ ${\sum }_i{x}_i$. We show that for every sparsef, and for all “typical”$$\mathcal { C}$$ $C$, faster#SAT algorithms for$$\mathcal { C}$$ $C$circuits imply lower bounds against the circuit class$$f \circ \mathcal { C}$$ $f\circ C$, which may bestrongerthan$$\mathcal { C}$$ $C$itself. In particular:#SAT algorithms forn^k-size$$\mathcal { C}$$ $C$-circuits running in 2ⁿ/n^ktime (for allk) implyNEXPdoes not have$$(f \circ \mathcal { C})$$ $(f\circ C)$-circuits of polynomial size.#SAT algorithms for$$2^{n^{{\varepsilon }}}$$ $2^{n^{\epsilon }}$-size$$\mathcal { C}$$ $C$-circuits running in$$2^{n-n^{{\varepsilon }}}$$ $2^{n-n^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$$(f \circ \mathcal { C})$$ $(f\circ C)$-circuits of polynomial size. Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJ∘ACC⁰∘THRcircuits of polynomial size, whereEMAJis the “exact majority” function, improving previous lower bounds againstACC⁰[Williams JACM’14] andACC⁰∘THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class. 

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5. Non-toric Brane Webs, Calabi–Yau 3-Folds, and 5d SCFTs

   https://doi.org/10.1007/s00220-025-05461-9  

   Alexeev, Valery; Argüz, Hülya; Bousseau, Pierrick (October 2025, Communications in Mathematical Physics)

   Abstract We study webs of 5-branes with 7-branes in Type IIB string theory from a geometric perspective. Mathematically, a web of 5-branes with 7-branes is a tropical curve in$$\mathbb {R}^2$$ $R^2$with focus-focus singularities introduced. To any such a webW, we attach a log Calabi–Yau surface (Y, D) with a line bundleL. We then describe supersymmetric webs, which are webs defining 5d superconformal field theories (SCFTs), in terms of the geometry of (Y, D, L). We also introduce particular supersymmetric webs called “consistent webs, and show that any 5d SCFT defined by a supersymmetric web can be obtained from a consistent web by adding free hypermultiplets. Using birational geometry of degenerations of log Calabi–Yau surfaces, we provide an algorithm to test the consistency of a web in terms of its dual polygon. Moreover, for a consistent webW, we provide an algebro-geometric construction of the mirror$$\mathcal {X}^{\textrm{can}}$$ $X^{\text{can}}$to (Y, D, L), as a non-toric canonical 3-fold singularity, and show that M-theory on$$\mathcal {X}^{\textrm{can}}$$ $X^{\text{can}}$engineers the same 5d SCFT asW. We also explain how to derive explicit equations for$$\mathcal {X}^{\textrm{can}}$$ $X^{\text{can}}$using scattering diagrams, encoding disk worldsheet instantons in the A-model, or equivalently the BPS states of an auxiliary rank one 4d$$\mathcal {N}=2$$ $N=2$theory. 

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