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1. Scattering from (p, q)-strings in AdS5 × S5

   https://doi.org/10.1007/JHEP03(2025)181  

   Pufu, Silviu S; Rodriguez, Victor A; Wang, Yifan (March 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> Motivated by understanding the scattering of gravitons and their superpartners from extended (p,q)-strings in type IIB string theory via AdS/CFT, we study an integrated two-point function of stress tensor multiplet operators in the presence of a half-BPS line defect in$$ \mathcal{N} $$ $N$= 4 SU(N) super-Yang-Mills theory. We determine this integrated correlator at the five lowest non-trivial orders in$$ 1/\sqrt{N} $$ $1/\sqrt{N}$at fixed Yang-Mills coupling andθangle. Our calculations are performed explicitly when the line defect is a Wilson line, in which case we find a finite number of perturbative contributions at each order in$$ 1/\sqrt{N} $$ $1/\sqrt{N}$, as well as instanton contributions. Using SL(2,ℤ) transformations, our results can also be applied to Wilson-’t Hooft line defects dual to extended (p,q)-strings in the bulk. We analyze features of these integrated correlators in the weak coupling expansion by comparing with open-closed amplitudes of type IIB string theory on AdS₅× S⁵, as well as in its flat space limit. We predict new higher-derivative interaction vertices on the D1-brane and, more generally, on (p,q)-strings. 

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2. Multipliers on bi-parameter Haar system Hardy spaces

   https://doi.org/10.1007/s00208-024-02887-9  

   Lechner, R.; Motakis, P.; Müller, P_F_X; Schlumprecht, Th (May 2024, Mathematische Annalen)

   Abstract Let$$(h_I)$$ $\left(h_I\right)$denote the standard Haar system on [0, 1], indexed by$$I\in \mathcal {D}$$ $I\in D$, the set of dyadic intervals and$$h_I\otimes h_J$$ $h_I\otimes h_J$denote the tensor product$$(s,t)\mapsto h_I(s) h_J(t)$$ $(s,t)\mapsto h_I\left(s\right)h_J\left(t\right)$,$$I,J\in \mathcal {D}$$ $I,J\in D$. We consider a class of two-parameter function spaces which are completions of the linear span$$\mathcal {V}(\delta ^2)$$ $V\left({\delta }^2\right)$of$$h_I\otimes h_J$$ $h_I\otimes h_J$,$$I,J\in \mathcal {D}$$ $I,J\in D$. This class contains all the spaces of the formX(Y), whereXandYare either the Lebesgue spaces$$L^p[0,1]$$ $L^p[0,1]$or the Hardy spaces$$H^p[0,1]$$ $H^p[0,1]$,$$1\le p < \infty $$ $1\le p<\infty$. We say that$$D:X(Y)\rightarrow X(Y)$$ $D:X\left(Y\right)\to X\left(Y\right)$is a Haar multiplier if$$D(h_I\otimes h_J) = d_{I,J} h_I\otimes h_J$$ $D(h_I\otimes h_J)=d_{I,J}{h}_I\otimes h_J$, where$$d_{I,J}\in \mathbb {R}$$ $d_{I,J}\in R$, and ask which more elementary operators factor throughD. A decisive role is played by theCapon projection$$\mathcal {C}:\mathcal {V}(\delta ^2)\rightarrow \mathcal {V}(\delta ^2)$$ $C:V\left({\delta }^2\right)\to V\left({\delta }^2\right)$given by$$\mathcal {C} h_I\otimes h_J = h_I\otimes h_J$$ $C{h}_I\otimes h_J=h_I\otimes h_J$if$$|I|\le |J|$$ $\left|I\right|\le \left|J\right|$, and$$\mathcal {C} h_I\otimes h_J = 0$$ $C{h}_I\otimes h_J=0$if$$|I| > |J|$$ $\left|I\right|>\left|J\right|$, as our main result highlights: Given any bounded Haar multiplier$$D:X(Y)\rightarrow X(Y)$$ $D:X\left(Y\right)\to X\left(Y\right)$, there exist$$\lambda ,\mu \in \mathbb {R}$$ $\lambda ,\mu \in R$such that$$\begin{aligned} \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C})\text { approximately 1-projectionally factors through }D, \end{aligned}$$ $\begin{array}{c}\lambda C+\mu (\text{Id}-C)\text{approximately 1-projectionally factors through}D,\end{array}$i.e., for all$$\eta > 0$$ $\eta >0$, there exist bounded operatorsA, Bso thatABis the identity operator$${{\,\textrm{Id}\,}}$$ $\text{Id}$,$$\Vert A\Vert \cdot \Vert B\Vert = 1$$ $\Vert A\Vert ·\Vert B\Vert =1$and$$\Vert \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C}) - ADB\Vert < \eta $$ $\Vert \lambda C+\mu (\text{Id}-C)-ADB\Vert <\eta$. Additionally, if$$\mathcal {C}$$ $C$is unbounded onX(Y), then$$\lambda = \mu $$ $\lambda =\mu$and then$${{\,\textrm{Id}\,}}$$ $\text{Id}$either factors throughDor$${{\,\textrm{Id}\,}}-D$$ $\text{Id}-D$. 

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3. BPS chaos

   https://doi.org/10.21468/SciPostPhys.18.2.072  

   Chen, Yiming; Lin, Henry W; Shenker, Steve (January 2025, SciPost Physics)

   Black holes are chaotic quantum systems that are expected to exhibit random matrix statistics in their finite energy spectrum. Lin, Maldacena, Rozenberg and Shan (LMRS) have proposed a related characterization of chaos for the ground states of BPS black holes with finite area horizons. On a separate front, the “fuzzball program” has uncovered large families of horizon-free geometries that account for the entropy of holographic BPS systems, but only in situations with sufficient supersymmetry to exclude finite area horizons. The highly structured, non-random nature of these solutions seems in tension with strong chaos. We verify this intuition by performing analytic and numerical calculations of the LMRS diagnostic in the corresponding boundary quantum system. In particular we examine the 1/2 and 1/4-BPS sectors of\mathcal{N}=4 $𝒩=4$SYM, and the two charge sector of the D1-D5 CFT. We find evidence that these systems are only weakly chaotic, with a Thouless time determining the onset of chaos that grows as a power ofN $N$. In contrast, finite horizon area BPS black holes should be strongly chaotic, with a Thouless time of order one. In this case, finite energy chaotic states become BPS asN $N$is decreased through the recently discovered “fortuity” mechanism. Hence they can plausibly retain their strongly chaotic character. 

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4. Construction of a Dirichlet form on Metric Measure Spaces of Controlled Geometry

   https://doi.org/10.1007/s11118-024-10144-6  

   Butaev, Almaz; Luo, Liangbing; Shanmugalingam, Nageswari (June 2024, Potential Analysis)

   Abstract Given a compact doubling metric measure spaceXthat supports a 2-Poincaré inequality, we construct a Dirichlet form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$that is comparable to the upper gradient energy form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$. Our approach is based on the approximation ofXby a family of graphs that is doubling and supports a 2-Poincaré inequality (see [20]). We construct a bilinear form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$using the Dirichlet form on the graph. We show that the$$\Gamma $$ $\Gamma$-limit$$\mathcal {E}$$ $E$of this family of bilinear forms (by taking a subsequence) exists and that$$\mathcal {E}$$ $E$is a Dirichlet form onX. Properties of$$\mathcal {E}$$ $E$are established. Moreover, we prove that$$\mathcal {E}$$ $E$has the property of matching boundary values on a domain$$\Omega \subseteq X$$ $\Omega \subseteq X$. This construction makes it possible to approximate harmonic functions (with respect to the Dirichlet form$$\mathcal {E}$$ $E$) on a domain inXwith a prescribed Lipschitz boundary data via a numerical scheme dictated by the approximating Dirichlet forms, which are discrete objects. 

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5. 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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