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1. Langevin dynamic for the 2D Yang–Mills measure

   https://doi.org/10.1007/s10240-022-00132-0  

   Chandra, Ajay; Chevyrev, Ilya; Hairer, Martin; Shen, Hao (June 2022, Publications mathématiques de l'IHÉS)

   Abstract We define a natural state space and Markov process associated to the stochastic Yang–Mills heat flow in two dimensions. To accomplish this we first introduce a space of distributional connections for which holonomies along sufficiently regular curves (Wilson loop observables) and the action of an associated group of gauge transformations are both well-defined and satisfy good continuity properties. The desired state space is obtained as the corresponding space of orbits under this group action and is shown to be a Polish space when equipped with a natural Hausdorff metric. To construct the Markov process we show that the stochastic Yang–Mills heat flow takes values in our space of connections and use the “DeTurck trick” of introducing a time dependent gauge transformation to show invariance, in law, of the solution under gauge transformations. Our main tool for solving for the Yang–Mills heat flow is the theory of regularity structures and along the way we also develop a “basis-free” framework for applying the theory of regularity structures in the context of vector-valued noise – this provides a conceptual framework for interpreting several previous constructions and we expect this framework to be of independent interest. 

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2. Three-dimensional imaging of pion using lattice QCD: generalized parton distributions

   https://doi.org/10.1007/JHEP02(2025)056  

   Ding, Heng-Tong; Gao, Xiang; Mukherjee, Swagato; Petreczky, Peter; Shi, Qi; Syritsyn, Sergey; Zhao, Yong (February 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> In this work, we report a lattice calculation ofx-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on anN_f= 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t. 

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3. All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories

   https://doi.org/10.1007/JHEP10(2024)221  

   Naculich, Stephen G; Osathapan, Athis (October 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop orderL) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers ofN). Using an iterative process, we systematically construct theL-loop color space of four-point amplitudes of fields in the adjoint representation of SU(N), SO(N), or Sp(N). We define the null space as the orthogonal complement of the color space. For SU(N), we confirm the existence of four independent null vectors (forL≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (forL≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory. 

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4. Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation

   https://doi.org/10.1007/JHEP04(2021)222  

   Anastasiou, Charalampos; Haindl, Rayan; Sterman, George; Yang, Zhou; Zeng, Mao (April 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract We study the singularity structure of two-loop QED amplitudes for the production of multiple off-shell photons in massless electron-positron annihilation and develop counterterms that remove their infrared and ultraviolet divergences point by point in the loop integrand. The remainders of the subtraction are integrable in four dimensions and can be computed in the future with numerical integration. The counterterms capture the divergences of the amplitudes and factorize in terms of the Born amplitude and the finite remainder of the one-loop amplitude. They consist of simple one- and two-loop integrals with at most three external momenta and can be integrated analytically in a simple manner with established methods. We uncover novel aspects of fully local IR factorization, where vertex and self energy subdiagrams must be modified by new symmetrizations over loop momenta, in order to expose their tree-like tensor structures and hence factorization of IR singularities prior to loop integration. This work is a first step towards isolating locally the hard contributions of generic gauge theory amplitudes and rendering them integrable in exactly four dimensions with numerical methods. 

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5. 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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