The role of Sp(2n) duality in quantum theory

TL;DR

This paper investigates how Sp(2n) duality symmetries influence the equivalence of different supergravity formulations, highlighting enhanced dualities in 4D and their implications for anomalies and UV divergences.

Contribution

It demonstrates the role of Sp(2n) duality in establishing S-matrix equivalence between supergravity types I and II across gauges, especially emphasizing the unique features in 4D.

Findings

Enhanced dualities exist in 4D supergravities.

Extra symmetries ensure S-matrix equivalence of different gauges.

Absence of enhanced dualities correlates with anomalies in higher dimensions.

Abstract

D-dimensional maximal supergravities type I with G/H coset spaces have global G-symmetry and local H symmetry, which can be gauge-fixed in symmetric or Iwasawa-type gauges. Maximal D-dimensional supergravities type II derived from higher dimensions without dualization have less local and global symmetries. In 4D, Gaillard-Zumino duality group Sp(56) enhances U-duality symmetry group $E_{7(7)}$. Using the Hamiltonian path integral, we show how extra symmetries beyond $E_{7(7)}$, serve to establish S-matrix equivalence of supergravities I and II in different gauges. Enhanced dualities are not available in D $> 4$. This is consistent with the existence of local H symmetry and global G symmetry anomalies and UV divergences in D $> 4$ supergravities, and with the absence of these anomalies and UV divergences, so far, in 4D ${\cal N}\geq 5$ supergravities.