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Embeddings of E(1,6) in E(5,10) and E(4,4)

Nicoletta Cantarini, Fabrizio Caselli, Victor Kac

Abstract

We study the embeddings of the exceptional infinite-dimensional Lie superalgebra E(1,6) in the exceptional Lie superalgebras E(5,10) and E(4,4). These questions arose in the recent works on enhanced symmetries in some supersymmetric theories by N. Garner, S. Raghavendran, I. Saberi and B. Williams.

Embeddings of E(1,6) in E(5,10) and E(4,4)

Abstract

We study the embeddings of the exceptional infinite-dimensional Lie superalgebra E(1,6) in the exceptional Lie superalgebras E(5,10) and E(4,4). These questions arose in the recent works on enhanced symmetries in some supersymmetric theories by N. Garner, S. Raghavendran, I. Saberi and B. Williams.

Paper Structure

This paper contains 4 sections, 12 theorems, 76 equations, 2 tables.

Table of Contents

  1. Introduction
  2. The exceptional Lie superalgebras $E(5,10)$, $E(4,4)$ and $E(1,6)$ and their principal gradings.
  3. Embedding the Lie superalgebra $E(1,6)$ into $E(5,10)$
  4. Embedding the Lie superalgebra $E(1,6)$ into $E(4,4)$

Key Result

Proposition 2.1

Let $0<k<n$ and $m>0$. Then

Theorems & Definitions (27)

  • Proposition 2.1
  • proof
  • Theorem 3.1
  • proof
  • Proposition 3.2
  • proof
  • Theorem 3.3
  • proof
  • Remark 4.1
  • Lemma 4.2
  • ...and 17 more