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1. Off-shell minimal form factors

   https://doi.org/10.1007/JHEP07(2025)231  

   Belitsky, A V; Bork, L V (July 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We study off-shelln-particle form factors of half-BPS operators built fromncomplex scalar fields at the two-loop order in the planar maximally supersymmetric Yang-Mills theory (sYM). These are known as minimal form factors. We construct their representation as a sum of independent scalar Feynman integrals relying on two complementary techniques. First, by going to the Coulomb branch of the theory by employing the spontaneous symmetry breaking which induces masses, but only for external particles while retaining masslessness for virtual states propagating in quantum loops. For a low number of external legs, this entails an uplift of massless integrands to their massive counterparts. Second, utilizing the$$ \mathcal{N} $$ $N$= 1 superspace formulation of$$ \mathcal{N} $$ $N$= 4 sYM and performing algebra of covariant derivatives off-shell. Both techniques provide identical results. These form factors are then studied in the near-mass-shell limit with the off-shellness regularizing emerging infrared divergences. We observe their exponentiation and confirm the octagon anomalous dimension, not the cusp, as the coefficient of the Sudakov double logarithmic behavior. By subtracting these singularities and defining a finite remainder, we verified that its symbol is identical to the one found a decade ago in the conformal case. Beyond-the-symbol contributions are different in the two cases, however. 

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2. 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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3. Ward identities for superamplitudes

   https://doi.org/10.1007/JHEP06(2024)035  

   Kallosh, Renata (June 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We introduce Ward identities for superamplitudes inD-dimensional$$ \mathcal{N} $$ $N$-extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for ann-partice superamplitude take a simple universal form for half BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of thensuperparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by (D− 2)L+ 2 −$$ \mathcal{N} $$ $N$or (D− 2)L+ 2 −$$ 2\mathcal{N} $$ $2N$, respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree. 

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4. Tree-level superstring amplitudes: the Neveu-Schwarz sector

   https://doi.org/10.1007/JHEP09(2024)008  

   Cacciatori, Sergio L; Grushevsky, Samuel; Voronov, Alexander A (September 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We present a complete computation of superstring scattering amplitudes at tree level, for the case of Neveu-Schwarz insertions. Mathematically, this is to say that we determine explicitly the superstring measure on the moduli space$$ {\mathcal{M}}_{0,n,0} $$ $M_{0,n,0}$of super Riemann surfaces of genus zero withn≥ 3 Neveu-Schwarz punctures. While, of course, an expression for the measure was previously known, we do this from first principles, using the canonically defined super Mumford isomorphism [1]. We thus determine the scattering amplitudes, explicitly in the global coordinates on$$ {\mathcal{M}}_{0,n,0} $$ $M_{0,n,0}$, without the need for picture changing operators or ghosts, and are also able to determine canonically the value of the coupling constant. Our computation should be viewed as a step towards performing similar analysis on$$ {\mathcal{M}}_{0,0,n} $$ $M_{0,0,n}$, to derive explicit tree-level scattering amplitudes with Ramond insertions. 

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5. 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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