Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

Abstract

The constraints imposed by maximal supersymmetry on multi-loop contributions to the scattering of four open superstrings in the U(N) theory are examined by use of the pure spinor formalism. The double-trace term k^2 t_8(tr F^2)^2 (where k represents an external momentum and F the Yang--Mills field strength) only receives contributions from L<=2 (where L is the loop number) while the single-trace term k^2 t_8(tr F^4) receives contributions from all L. We verified these statements up to L=5, but arguments based on supersymmetry suggest they extend to all L. This explains why the single-trace contributions to low energy maximally supersymmetric Yang--Mills field theory are more divergent in the ultraviolet than the double-trace contributions. We also comment further on the constraints on closed string amplitudes and their implications for ultraviolet divergences in N=8 supergravity.

25 pages. 2 eps figures. Harvmac format. v2 qualifications regarding comments on closed strings. References added

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Cited by in corpus (35)

• On D=5 super Yang-Mills theory and (2,0) theory
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• E7(7) constraints on counterterms in N=8 supergravity
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• The closed-string 3-loop amplitude and S-duality
• String theory dualities and supergravity divergences
• Supertwistor space for 6D maximal super Yang-Mills
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• 5 loops in 24/5 dimensions
• The vanishing volume of D=4 superspace
• A simple approach to counterterms in N=8 supergravity
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Higher-loop amplitude monodromy relations in string and gauge theory
• Tropical Amplitudes
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• BCJ duality and double copy in the closed string sector
• Simplifying the Tree-level Superstring Massless Five-point Amplitude
• Tree-level amplitudes from the pure spinor superstring
• Tetrahedral modular graph functions
• Integral invariants in maximally supersymmetric Yang-Mills theories
• Pure spinor superfields and Born-Infeld theory
• SUSY Ward identities, Superamplitudes, and Counterterms
• Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace
• Gravitino Interactions from Yang-Mills Theory
• Type I/heterotic duality and M-theory amplitudes
• The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• An off-shell superspace reformulation of D=4, N=4 super-Yang-Mills theory
• Non-analytic terms of string amplitudes from partial waves
• Higher-dimensional invariants in $6D$ super Yang-Mills theory
• Off- and on-shell harmonic superspaces for 6D SYM theories