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U-duality and non-BPS solutions

Gianguido Dall'Agata, Stefano Giusto, Clement Ruef

TL;DR

The paper reveals how the U-duality group of the STU model maps BPS and non-BPS extremal multicenter solutions, deriving explicit transformations via six T-dualities and four-dimensional symplectic rotations. It shows that the non-BPS class is not closed under U-duality, enabling the generation of new under-rotating solutions such as rotating black strings and Israel–Wilson-based geometries from known seeds. A key result is the identification of spectral flow as a conjugation of large gauge transformations by T-dualities, clarifying its place inside the U-duality group. The work provides a concrete framework to construct general non-BPS multicenter configurations, with potential implications for microstate geometries and the broader landscape of extremal solutions in string theory. Overall, it connects 10D and 4D perspectives, illustrating how dualities expand the space of physically distinct non-BPS extremal solutions in the STU model.

Abstract

We derive the explicit action of the U-duality group of the STU model on both BPS and non-BPS extremal multi-center solutions. As the class of known non-BPS extremal solutions is not closed under U-duality, we generate in this way new solutions. These should represent the most general class of extremal non-BPS multi-center under-rotating solutions of the STU model.

U-duality and non-BPS solutions

TL;DR

The paper reveals how the U-duality group of the STU model maps BPS and non-BPS extremal multicenter solutions, deriving explicit transformations via six T-dualities and four-dimensional symplectic rotations. It shows that the non-BPS class is not closed under U-duality, enabling the generation of new under-rotating solutions such as rotating black strings and Israel–Wilson-based geometries from known seeds. A key result is the identification of spectral flow as a conjugation of large gauge transformations by T-dualities, clarifying its place inside the U-duality group. The work provides a concrete framework to construct general non-BPS multicenter configurations, with potential implications for microstate geometries and the broader landscape of extremal solutions in string theory. Overall, it connects 10D and 4D perspectives, illustrating how dualities expand the space of physically distinct non-BPS extremal solutions in the STU model.

Abstract

We derive the explicit action of the U-duality group of the STU model on both BPS and non-BPS extremal multi-center solutions. As the class of known non-BPS extremal solutions is not closed under U-duality, we generate in this way new solutions. These should represent the most general class of extremal non-BPS multi-center under-rotating solutions of the STU model.

Paper Structure

This paper contains 26 sections, 189 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The setup
  3. The 11-dimensional ansatz
  4. Fields in type IIA
  5. Fields in 4-dimensional $N=2$ supergravity
  6. The BPS case
  7. The almost-BPS case
  8. T-dualities and Buscher's rules
  9. Dualities and the BPS solutions
  10. The BPS black string
  11. Gauge transformations, T-dualities and spectral flow
  12. T-dualities and the almost BPS solutions
  13. T-dualities, gauge transformations and spectral flows in the non-BPS case
  14. Generic Calabi--Yau compactifications
  15. Interesting subcases after 6 T-dualities
  16. ...and 11 more sections

Figures (1)

  • Figure 1: We depict the commutative diagram expressing the link between spectral flow, large gauge transformations and T-duality. If one starts from a given BPS solution (solution 1), one can perform 6 T-dualities on it to obtain solution 2. On the other hand, one can first perform a large gauge transformation \ref{['ggetsfoBPS']} on solution 1 to obtain solution 1', that only differs from solution 1 by the values of the B-field Wilson lines. If one then perform 6 T-dualities on solution 1', one obtains solution 3. Solution 2 and solution 3 are related by a spectral flow transformation Bena:2008wt.