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D=10 supersymmetric Yang-Mills theory at alpha'^4

P. S. Howe, U. Lindstrom, L. Wulff

TL;DR

The paper tackles the problem of extending the $D=10$ SYM deformation to order $\alpha'^4$ in a non-abelian setting while preserving maximal supersymmetry.It combines spinorial cohomology and a generalized superembedding approach to construct the dimension-zero constraint corrections $F_{\alpha\beta}=F_{0,2}^{SE}+F^{2}_{\alpha\beta}$, identifying necessary higher-derivative and commutator terms beyond the symmetrised Born–Infeld piece.The authors show that the superembedding result is nearly complete but misses certain two- and four-commutator contributions; these are supplied by two higher-derivative/commutator corrections $F^{HD1}$ and $F^{HD2}$, leading to a full $F_{0,2}^2$ given by $9F^{SE}+F^{HD1}+F^{HD2}$ and compatible with the $D=10$ SYM cohomology constraints.They also connect the action to the ectoplasm formalism, requiring a Weil-trivial combination of two closed 11-forms $W$ and $W'$ to account for $\alpha'^4$ corrections, and discuss the abelian limit where the result reduces to a $\partial^4F^4$-type term.

Abstract

The $α'^2$ deformation of D=10 SYM is the natural generalisation of the $F^4$ term in the abelian Born-Infeld theory. It is shown that this deformation can be extended to $α'^4$ in a way which is consistent with supersymmetry. The latter requires the presence of higher-derivative and commutator terms as well as the symmetrised trace of the Born-Infeld $α'^4$ term.

D=10 supersymmetric Yang-Mills theory at alpha'^4

TL;DR

The paper tackles the problem of extending the $D=10$ SYM deformation to order $\alpha'^4$ in a non-abelian setting while preserving maximal supersymmetry.It combines spinorial cohomology and a generalized superembedding approach to construct the dimension-zero constraint corrections $F_{\alpha\beta}=F_{0,2}^{SE}+F^{2}_{\alpha\beta}$, identifying necessary higher-derivative and commutator terms beyond the symmetrised Born–Infeld piece.The authors show that the superembedding result is nearly complete but misses certain two- and four-commutator contributions; these are supplied by two higher-derivative/commutator corrections $F^{HD1}$ and $F^{HD2}$, leading to a full $F_{0,2}^2$ given by $9F^{SE}+F^{HD1}+F^{HD2}$ and compatible with the $D=10$ SYM cohomology constraints.They also connect the action to the ectoplasm formalism, requiring a Weil-trivial combination of two closed 11-forms $W$ and $W'$ to account for $\alpha'^4$ corrections, and discuss the abelian limit where the result reduces to a $\partial^4F^4$-type term.

Abstract

The deformation of D=10 SYM is the natural generalisation of the term in the abelian Born-Infeld theory. It is shown that this deformation can be extended to in a way which is consistent with supersymmetry. The latter requires the presence of higher-derivative and commutator terms as well as the symmetrised trace of the Born-Infeld term.

Paper Structure

This paper contains 26 sections, 121 equations.

Table of Contents

  1. Introduction
  2. Conventions and tools
  3. $\mathcal{N}=1$ superspace
  4. Conventions for super Yang-Mills
  5. Superspace cohomology
  6. Deformations of SYM
  7. Lowest order or pure super Yang-Mills
  8. First correction (order $\alpha'^2$)
  9. Induced terms at second order ($\alpha'^4$)
  10. Comparison to the superembedding approach
  11. Terms at order $\alpha'^4$ coming from the superembedding approach
  12. Higher derivative/commutator terms
  13. The remaining terms in $F_{0,2}^2$
  14. Action form
  15. Conclusions
  16. ...and 11 more sections