Weyl Groups in AdS(3)/CFT(2)

TL;DR

This paper explores the residual U-duality symmetries in D1-D5-KK brane systems and their implications for the AdS(3)/CFT(2) correspondence, revealing how these symmetries influence marginal operators in the dual CFT.

Contribution

It identifies the residual U-duality group as a lift of the Weyl group of F_{4(+4)} and demonstrates its enhancement to F_{4(+4)}(Z) when charges coincide, applying this to CFT operator analysis.

Findings

Residual U-duality symmetry is a lift of the Weyl group of F_{4(+4)}.

Symmetry enhancement occurs when all three charges are equal.

16 out of 28 marginal operators are exactly marginal under the residual symmetry.

Abstract

The system of D1 and D5 branes with a Kaluza-Klein momentum is re-investigated using the five-dimensional U-duality group E_{6(+6)}(Z). We show that the residual U-duality symmetry that keeps this D1-D5-KK system intact is generically given by a lift of the Weyl group of F_{4(+4)}, embedded as a finite subgroup in E_{6(+6)}(Z). We also show that the residual U-duality group is enhanced to F_{4(+4)}(Z) when all the three charges coincide. We then apply the analysis to the AdS(3)/CFT(2) correspondence, and discuss that among 28 marginal operators of CFT(2) which couple to massless scalars of AdS(3) gravity at boundary, 16 would behave as exactly marginal operators for generic D1-D5-KK systems. This is shown by analyzing possible three-point couplings among 42 Kaluza-Klein scalars with the use of their transformation properties under the residual U-duality group.