In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
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Transcendentality and Crossing
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abstract
We discuss possible phase factors for the S-matrix of planar N=4 gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN-scaling, Kotikov-Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS_5xS^5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.
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Presents the zeta(3)-proportional term of the four-loop non-singlet twist-two quark anomalous dimension for general N in closed form, extracted via analytic reconstruction from published Mellin moments.
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Conjecture that the three-point structure constant of one single-trace and two determinant operators in N=4 SYM is given by glued hexagon form factors, reducing to partition sums with reflections at weak coupling and matching explicit tree-level computations.
One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
High-energy string amplitudes have asymptotic expansions governed by Bernoulli numbers, upgraded via resurgence to transseries whose Stokes data encode non-perturbative monodromy between kinematic regions.
Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
Eight-loop computation of the tr φ³ three-point form factor in planar N=4 SYM together with coefficient patterns in its symbol.
The strong-coupling transseries for matrix Bessel determinant observables is generated from its perturbative part by shifting a→a−Δ and replacing moments I_n, with all Stokes constants fixed by two recurrences.
In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equations, enabling a chi-system for both polygonal and closed geometries.
Conjecture predicts all-loop double-log null-limit behavior of n-point large-charge correlators in planar N=4 SYM via the tilted cusp anomalous dimension, matching small-mass massive amplitudes.
Explicit two-loop computations of protected correlators in N=4 SYM yield a universal one-loop term and a planar extrapolation at arbitrary dimension controlled by stress-tensor multiplet count.
Finite-loop truncations of the planar dilatation operator in N=4 SYM exhibit GOE-like level statistics at large coupling for two- and four-loops (but not three), with eigenvector and Krylov diagnostics indicating weak integrability breaking and multifractality.
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
Resurgent methods applied to perturbative expansions of the tilted cusp anomalous dimension yield non-perturbative information and identify governing singularities.
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Walking Sudakov: From Cusp to Octagon
In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
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Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
Presents the zeta(3)-proportional term of the four-loop non-singlet twist-two quark anomalous dimension for general N in closed form, extracted via analytic reconstruction from published Mellin moments.
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On the $AdS_3\times S^3\times S^3\times S^1$ dressing factors
Dressing factors are proposed for the S-matrix of massive worldsheet excitations in AdS3×S3×S3×S1 with mixed RR/NSNS flux that satisfy crossing, unitarity, and reproduce perturbative results for any radius ratio.
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Structure Constants of a Single Trace Operator and Determinant Operators from Hexagon
Conjecture that the three-point structure constant of one single-trace and two determinant operators in N=4 SYM is given by glued hexagon form factors, reducing to partition sums with reflections at weak coupling and matching explicit tree-level computations.
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Landau Analysis of One-Cycle Negative Geometries
One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
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Resurgence of high-energy string amplitudes
High-energy string amplitudes have asymptotic expansions governed by Bernoulli numbers, upgraded via resurgence to transseries whose Stokes data encode non-perturbative monodromy between kinematic regions.
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Positivity properties of observables in planar maximally supersymmetric Yang-Mills theory
Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
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Eight loop form factors, amplitudes and patterns in planar $\mathcal{N}=4$ super-Yang-Mills theory
Eight-loop computation of the tr φ³ three-point form factor in planar N=4 SYM together with coefficient patterns in its symbol.
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Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel
The strong-coupling transseries for matrix Bessel determinant observables is generated from its perturbative part by shifting a→a−Δ and replacing moments I_n, with all Stokes constants fixed by two recurrences.
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Classical correlation functions at strong coupling from hexagonalization
In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equations, enabling a chi-system for both polygonal and closed geometries.
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Null limit of large-charge correlators in planar $\mathcal{N}=4$ Super-Yang-Mills theory
Conjecture predicts all-loop double-log null-limit behavior of n-point large-charge correlators in planar N=4 SYM via the tilted cusp anomalous dimension, matching small-mass massive amplitudes.
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Tracing Transcendentality in Protected Correlators of N=4 SYM
Explicit two-loop computations of protected correlators in N=4 SYM yield a universal one-loop term and a planar extrapolation at arbitrary dimension controlled by stress-tensor multiplet count.
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Probing weak chaos in $\mathcal N=4$ super Yang-Mills and long-range spin chains
Finite-loop truncations of the planar dilatation operator in N=4 SYM exhibit GOE-like level statistics at large coupling for two- and four-loops (but not three), with eigenvector and Krylov diagnostics indicating weak integrability breaking and multifractality.
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Multi-Loop Negative Geometries
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
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Resurgence of the Tilted Cusp Anomalous Dimension
Resurgent methods applied to perturbative expansions of the tilted cusp anomalous dimension yield non-perturbative information and identify governing singularities.