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One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills Theories

Mingxing Luo, Congkao Wen

TL;DR

The paper tests the Cachazo–Svrcek–Witten (CSW) construction for one-loop maximal helicity violating (MHV) amplitudes in N=4 Super Yang–Mills, extending beyond the large-$N_c$ limit. It verifies that leading and sub-leading color amplitudes $A_{n;1}$ and $A_{n;c}$ produced by CSW match conventional field-theory results for all external multiplicities $n$ by relating sub-leading diagrams to permutations of leading ones. The authors provide explicit checks for four- and five-point cases and then a general proof for arbitrary $n$, showing that sub-leading MHV diagrams can be expressed as sums of leading MHV diagrams. The results establish the CSW approach as a valid one-loop tool for MHV amplitudes in finite-$N_c$ theories and motivate further exploration of its theoretical foundation and extensions to non-MHV sectors.

Abstract

One-loop maximal helicity violating (MHV) amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and Witten (CSW). The relations between leading N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;c} obtained by the CSW prescription are found to be identical to those obtained from conventional field theory calculations. Combining with existing results, this establishes the validity of the CSW prescription to one-loop in the calculation of MHV amplitudes in N=4 SYM theories of finite N_c.

One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills Theories

TL;DR

The paper tests the Cachazo–Svrcek–Witten (CSW) construction for one-loop maximal helicity violating (MHV) amplitudes in N=4 Super Yang–Mills, extending beyond the large- limit. It verifies that leading and sub-leading color amplitudes and produced by CSW match conventional field-theory results for all external multiplicities by relating sub-leading diagrams to permutations of leading ones. The authors provide explicit checks for four- and five-point cases and then a general proof for arbitrary , showing that sub-leading MHV diagrams can be expressed as sums of leading MHV diagrams. The results establish the CSW approach as a valid one-loop tool for MHV amplitudes in finite- theories and motivate further exploration of its theoretical foundation and extensions to non-MHV sectors.

Abstract

One-loop maximal helicity violating (MHV) amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and Witten (CSW). The relations between leading N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;c} obtained by the CSW prescription are found to be identical to those obtained from conventional field theory calculations. Combining with existing results, this establishes the validity of the CSW prescription to one-loop in the calculation of MHV amplitudes in N=4 SYM theories of finite N_c.

Paper Structure

This paper contains 5 sections, 37 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Review of existing one-loop results and the CSW prescription
  3. Special cases of four and five external particles
  4. General cases of arbitrary number of external particles
  5. Conclusion

Figures (9)

  • Figure 1: One leading order one-loop MHV diagram, using MHV amplitudes as interaction vertices, with the CSW off-shell prescription.
  • Figure 2: A one-loop MHV diagram with one three-leg MHV vertex, shown to give a null result.
  • Figure 3: (a) Leading one-loop MHV diagrams for the special case of four external particles.
  • Figure 3: (b) Sub-leading one-loop MHV diagrams for the special case of four external particles.
  • Figure 4: The topologies for leading (top) and sub-leading (bottom) one-loop MHV diagrams for the special case of five external particles.
  • ...and 4 more figures