[Paper Review] Strings, Branes and the Self-dual Solutions of Exceptional Field Theory

David S. Berman, Felix J. Rudolph|arXiv (Cornell University)|Dec 8, 2014

Black Holes and Theoretical Physics45 references4 citations

TL;DR

This paper presents a single self-dual solution in Exceptional Field Theory (EFT) that unifies fundamental strings, membranes, fivebranes, and D-branes as different reductions of one object. By solving a twisted self-duality constraint, the solution geometrically realizes the 1/2 BPS spectrum of 10D and 11D supergravity, with duality transformations arising from different compactifications of the same underlying solution.

ABSTRACT

It has been shown that membranes and fivebranes are wave-like or monopole-like solutions in some higher dimensional theory. Here the picture is completed by combining the wave and monopole solutions into a single solution of Exceptional Field Theory. This solution solves the twisted self-duality constraint. The 1/2 BPS brane spectrum, consisting of fundamental, solitonic and Dirichlet branes, in ten- and eleven-dimensional supergravity may all be extracted from this single solution of Exceptional Field Theory. The solution's properties such as the singularity structure and its asymptotic behaviour near the core and at infinity are investigated.

Motivation & Objective

• To unify the 1/2 BPS brane spectrum of 10D and 11D supergravity into a single solution within Exceptional Field Theory.
• To demonstrate that U-duality transformations among branes arise from different compactifications of one self-dual solution.
• To show that the solution satisfies a twisted self-duality constraint and geometrically realizes electric-magnetic duality.
• To analyze the solution's asymptotic and core behavior under various reductions.
• To provide a geometric realization of the duality group action as relabeling of compactification cycles.

Proposed method

• Constructing a solution in E7(7) Exceptional Field Theory that satisfies the twisted self-duality constraint using a harmonic function and a quantized parameter.
• Embedding eleven-dimensional and ten-dimensional supergravity solutions into the EFT framework via consistent truncations.
• Using KK-decomposition to reduce the EFT solution to lower-dimensional brane solutions by compactifying on different cycles.
• Applying the physical section condition to ensure consistency of the reduction to physical spacetime.
• Mapping the gauge fields and metric components of EFT to known brane solutions in 10D and 11D supergravity.
• Analyzing the solution's behavior at infinity and at the core to understand its physical interpretation across reductions.

Experimental results

Research questions

• RQ1 How can a single solution in Exceptional Field Theory reproduce all 1/2 BPS branes in 10D and 11D supergravity?
• RQ2 What is the role of the twisted self-duality constraint in unifying wave and monopole solutions?
• RQ3 How do duality transformations among branes emerge from a single geometric object in EFT?
• RQ4 What is the asymptotic and core structure of the EFT solution under different compactifications?
• RQ5 How does the solution realize electric-magnetic duality in the reduced theories?

Key findings

• The EFT solution is a superposition of a wave and a monopole with a single quantized parameter that encodes both momentum and charge.
• The solution satisfies a twisted self-duality constraint, generalizing the self-dual string in the (0,2) theory to supergravity.
• All 1/2 BPS states—fundamental strings, membranes, fivebranes, D-branes, and their bound states—arise as reductions of this single solution.
• The duality group action on the brane spectrum is realized as relabeling of compactification cycles in the extended EFT space.
• At infinity, the solution asymptotes to a wave or monopole depending on the reduction, while at the core, it exhibits a non-trivial geometric structure.
• The solution's metric and gauge fields reduce consistently to known supergravity solutions, including the Dp-brane for p=0,…,6, with correct dilaton and harmonic function dependence.