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The chiral ring of D=4, N=1 SYM with exceptional gauge groups

Martin Cederwall, Gabriele Ferretti

Abstract

The Cachazo-Douglas-Seiberg-Witten conjecture, concerning the algebraic structure of the chiral ring in N=1, D=4 supersymmetric Yang-Mills theory, is proven for exceptional gauge groups. This completes the proof of the conjecture.

The chiral ring of D=4, N=1 SYM with exceptional gauge groups

Abstract

The Cachazo-Douglas-Seiberg-Witten conjecture, concerning the algebraic structure of the chiral ring in N=1, D=4 supersymmetric Yang-Mills theory, is proven for exceptional gauge groups. This completes the proof of the conjecture.
Paper Structure (6 sections, 6 theorems, 7 equations)

This paper contains 6 sections, 6 theorems, 7 equations.

Table of Contents

  1. The content of ${\mathfrak g}$-modules in $B$ for exceptional ${\mathfrak g}$
  2. $G_2$
  3. $F_4$
  4. $E_6$
  5. $E_7$
  6. $E_8$

Key Result

Lemma 1

The multiplication table of irreducible modules in $B$ and that of $(B\times B)^{\mathfrak g}$ contain the same structure constants. Let $X_iX_j=\sum_kc_{ij}{}^kX_k$. Then, $S_iS_j=(-1)^{n_in_j}\sum_kc_{ij}{}^kS_k$.

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Corollary 1
  • Proposition 1
  • Corollary 2
  • Proposition 2
  • proof
  • Theorem 1