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1. Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality

   https://doi.org/10.1007/JHEP02(2021)139  

   D’Hoker, Eric; Mafra, Carlos R.; Pioline, Boris; Schlotterer, Oliver (February 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract In an earlier paper, we constructed the genus-two amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the α ′ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1) R -preserving amplitudes such as for five gravitons, and for U(1) R -violating amplitudes such as for one dilaton and four gravitons. At each order in α ′, the coefficients of the effective interactions are given by integrals over moduli space of genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading orders, the coefficients of the effective interactions D 2 ℛ 5 and D 4 ℛ 5 are found to match those of D 4 ℛ 4 and D 6 ℛ 4 , respectively, as required by non-linear supersymmetry. To the next order, a D 6 ℛ 5 effective interaction arises, which is independent of the supersymmetric completion of D 8 ℛ 4 , and already arose at genus one. A novel identity on genus-two modular graph functions, which we prove, ensures that up to order D 6 ℛ 5 , the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1) R -violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector. 

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2. An off-shell Wilson loop

   https://doi.org/10.1007/JHEP04(2023)071  

   Belitsky, A. V.; Smirnov, V. A. (April 2023, Journal of High Energy Physics)

   A bstract It is well-known that on-shell maximally helicity-violating gluon scattering amplitudes in planar maximally supersymmetric Yang-Mills theory are dual to a bosonic Wilson loop on a null-polygonal contour. The light-like nature of the intervals is a reflection of the mass-shell condition for massless gluons involved in scattering. Presently, we introduce a Wilson loop prototype on a piece-wise curvilinear contour that can be interpreted in the T-dual language to correspond to nonvanishing gluon off-shellness. We analyze it first for four sites at one loop and demonstrate that it coincides with the four-gluon amplitude on the Coulomb branch. Encouraged by this fact, we move on to the two-loop order. To simplify our considerations, we only focus on the Sudakov asymptotics of the Wilson loop, when the off-shellness goes to zero. The latter serves as a regulator of short-distance divergences around the perimeter of the loop, i.e., divergences when gluons are integrated over a small vicinity of the Wilson loop cusps. It does not however regulate conventional ultraviolet divergences of interior closed loops. This unavoidably introduces a renormalization scale dependence and thus scheme dependence into the problem. With a choice of the scale setting and a finite renormalization, we observe exponentiation of the double logarithmic scaling of the Wilson loop with the accompanying exponent being given by the so-called hexagon anomalous dimension, which recently made its debut in the origin limit of six-leg gluon amplitudes. This is contrary to the expectation for the octagon anomalous dimension to rather emerge from our analysis suggesting that the current object encodes physics different from the Coulomb branch scattering amplitudes. 

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3. Local infrared safety in time-ordered perturbation theory

   https://doi.org/10.1007/JHEP02(2024)101  

   Sterman, George; Venkata, Aniruddha (February 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We develop a general expression for weighted cross sections in leptonic annihilation to hadrons based on time-ordered perturbation theory (TOPT). The analytic behavior of the resulting integrals over spatial momenta can be analyzed in the language of Landau equations and infrared (IR) power counting. For any infrared-safe weight, the cancellation of infrared divergences is implemented locally at the integrand level, and in principle can be evaluated numerically in four dimensions. We go on to show that it is possible to eliminate unphysical singularities that appear in time-ordered perturbation theory for arbitrary amplitudes. This is done by reorganizing TOPT into an equivalent form that combines classes of time orderings into a “partially time-ordered perturbation theory”. Applying the formalism to leptonic annihilation, we show how to derive diagrammatic expressions with only physical unitarity cuts. 

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4. All-loop-orders relation between Regge limits of $$ \mathcal{N} $$ = 4 SYM and $$ \mathcal{N} $$ = 8 supergravity four-point amplitudes

   https://doi.org/10.1007/JHEP02(2021)044  

   Naculich, Stephen G. (February 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract We examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ N = 4 SYM four-point amplitude. We begin by developing a basis of color factors C ik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through $$ \mathcal{O}\left({\upepsilon}^2\right) $$ O ϵ 2 at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ O ϵ 0 at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the $$ \mathcal{N} $$ N = 8 supergravity four-point amplitude. 

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5. Proof of a three-loop relation between the Regge limits of four-point amplitudes in $$ \mathcal{N} $$ = 4 SYM and $$ \mathcal{N} $$ = 8 supergravity

   https://doi.org/10.1007/JHEP07(2022)043  

   Naculich, Stephen G.; Wecker, Theodore W. (July 2022, Journal of High Energy Physics)

   A bstract A previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory and $$ \mathcal{N} $$ N = 8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered. 

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