Schubert line defects in 3d GLSMs. Part I. Complete flag manifolds and quantum Grothendieck polynomials

Journal article

Recently proposed exceptional field theories (EFTs) making manifest the duality $E_{n(n)}$ symmetry, first observed as nonlinearly realized symmetries of the maximal $d=3,4,...,9$ supergravity ($n=11-d$) and containing 11D and type IIB supergravity as sectors, were formulated in enlarged spacetimes. In the case of $E_{7(7)}$ EFT such an enlarged spacetime can be identified with the bosonic body of the $d=4$ central charge superspace $\Sigma^{(60|32)}$, the ${\cal N}=8$ $d=4$ superspace completed by 56 additional bosonic coordinates associated to central charges of the maximal $d=4$ supersymmetry algebra. In this paper we show how the hypothesis on the relation of all the known $E_{n(n)}$ EFTs, including $n=8$, with supersymmetry leads to the conjecture on existence of 11D exceptional field theory living in 11D tensorial central charge superspace $\Sigma^{(528|32)}$ and underlying all the $E_{n(n)}$ EFTs with $n=2,...,8$, and probably the double field theory (DFT). We conjecture the possible form of the section conditions of such an 11D EFT and show that quite generic solutions of these can be generated by superparticle models the ground states of which preserve from one half to all but one supersymmetry. The properties of these superparticle models are briefly discussed. We argue that, upon quantization, their quantum states should describe free massless non-conformal higher spin fields in D=11. We also discuss some relevant representations of the M-theory superalgebra which, in the present context, describes supersymmetry of the 11D EFT.Comment: 33 pages. V2: references added. V3: 42 pages. Minor corrections. New sections 3.3 and 5 added. Published in NP

Authors: Closset, C; Gu, W; Khlaif, O; Sharpe, E; Zhang, H

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2026
• Issue: 4
• Pages: 74
• Publication date: 2026-04-10
• DOI: 10.1007/jhep04(2026)074
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Flag (linear algebra); Quiver; Quantum; Realization (probability); Sigma model; Schubert variety; Gauge theory; Line (geometry); Grassmannian