Abstract
In this paper, the \( \mathcal{A} \)-theory, an extension of F-theory, is described as a fully U-duality covariant brane theory. This theory has some distinguishing features not known from world-sheet models. In particular, seen as a sigma model, both world-volume and target space coordinates are specific representations of the same group (the U-duality group). The U-duality group in question is an exceptional group (a split form of the Ed series). The structure of this group allows it to encompass both the T-duality group of string theory as well as the general linear symmetry group of \( \mathcal{M} \)-theory. \( \mathcal{A} \)-theory is defined by the current algebras in Hamiltonian formalism, or by world-volume actions in Lagrangian formalism. The spacetime coordinates are selfdual gauge fields on the world-volume, requiring the Gauß law constraints tying the world-volume to spacetime. Solving the Gauß law constraints/the Virasoro constraints gives the world-volume/spacetime sectioning from \( \mathcal{A} \)-theory to \( \mathcal{T} \)-theory/\( \mathcal{M} \)-theory respectively. The \( \mathcal{A} \)-theory Lagrangian admits extended symmetry which has not been observed previously in the literature, where the background fields include both the spacetime and the world-volume gravitational fields. We also constructed the four-point amplitude of \( \mathcal{A} \)-theory in the low energy limit. The amplitude is written in a way that the U-duality symmetry is manifest, but after solving the section condition, it reduces to the usual four-graviton amplitude.
In the previous papers, we have referred to this model as F-theory, however, F-theory initiated by Vafa is now a big branch of string theory as the study of elliptic fibrations, so we refer to these constructions as generalized models of theory for all dimensions with all duality symmetries as \( \mathcal{A} \)-theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
C. Vafa, Evidence for F theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
W. Siegel, Manifest duality in low-energy superstrings, in the proceedings of the International Conference on Strings 93, (1993) [hep-th/9308133] [INSPIRE].
A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].
M.J. Duff, E8 x SO(16) symmetry of d = 11 supergravity, CERN-TH-4124/85 (1985) [INSPIRE].
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].
M. Poláček and W. Siegel, T-duality off shell in 3D Type II superspace, JHEP 06 (2014) 107 [arXiv:1403.6904] [INSPIRE].
I.I.I.W.D. Linch and W. Siegel, F-theory from Fundamental Five-branes, JHEP 02 (2021) 047 [arXiv:1502.00510] [INSPIRE].
W.D. Linch and W. Siegel, F-theory with Worldvolume Sectioning, JHEP 04 (2021) 022 [arXiv:1503.00940] [INSPIRE].
D.S. Berman, C.D.A. Blair, E. Malek and F.J. Rudolph, An action for F-theory: SL(2)ℝ+ exceptional field theory, Class. Quant. Grav. 33 (2016) 195009 [arXiv:1512.06115] [INSPIRE].
L. Chabrol, Geometry of ℝ+ × E3(3) exceptional field theory and F-theory, JHEP 08 (2019) 073 [arXiv:1901.08295] [INSPIRE].
W. Siegel, F-theory with zeroth-quantized ghosts, arXiv:1601.03953 [INSPIRE].
W. Siegel and Y.-P. Wang, F-theory amplitudes, arXiv:2010.14590 [INSPIRE].
C.-Y. Ju and W. Siegel, Gauging Unbroken Symmetries in F-theory, Phys. Rev. D 94 (2016) 106004 [arXiv:1607.03017] [INSPIRE].
W. Siegel and D. Wang, M Theory from F Theory, arXiv:2010.09564 [INSPIRE].
W. Linch and W. Siegel, F-brane Superspace: The New World Volume, arXiv:1709.03536 [INSPIRE].
W.D. Linch and W. Siegel, F-brane Dynamics, arXiv:1610.01620 [INSPIRE].
W.D. Linch and W. Siegel, Critical Super F-theories, arXiv:1507.01669 [INSPIRE].
W. Siegel and D. Wang, Enlarged exceptional symmetries of first-quantized F-theory, arXiv:1806.02423 [INSPIRE].
W.D. Linch and W. Siegel, F-theory superspace, JHEP 03 (2021) 059 [arXiv:1501.02761] [INSPIRE].
W. Siegel and D. Wang, F-theory superspace backgrounds, arXiv:1910.01710 [INSPIRE].
M. Hatsuda and W. Siegel, Perturbative F-theory 10-brane and M-theory 5-brane, JHEP 11 (2021) 201 [arXiv:2107.10568] [INSPIRE].
M. Hatsuda and W. Siegel, Open F-branes, JHEP 04 (2022) 073 [arXiv:2110.13010] [INSPIRE].
T. Weigand, F-theory, PoS TASI2017 (2018) 016 [arXiv:1806.01854] [INSPIRE].
M. Poláček and W. Siegel, Pre-potential in the AdS5 × S5 Type IIB superspace, JHEP 01 (2017) 059 [arXiv:1608.02036] [INSPIRE].
M. Hatsuda, K. Kamimura and W. Siegel, Superspace with manifest T-duality from type II superstring, JHEP 06 (2014) 039 [arXiv:1403.3887] [INSPIRE].
M. Hatsuda, K. Kamimura and W. Siegel, Ramond-Ramond gauge fields in superspace with manifest T-duality, JHEP 02 (2015) 134 [arXiv:1411.2206] [INSPIRE].
M. Hatsuda, K. Kamimura and W. Siegel, Type II chiral affine Lie algebras and string actions in doubled space, JHEP 09 (2015) 113 [arXiv:1507.03061] [INSPIRE].
M. Hatsuda and K. Kamimura, SL(5) duality from canonical M2-brane, JHEP 11 (2012) 001 [arXiv:1208.1232] [INSPIRE].
M. Hatsuda and K. Kamimura, M5 algebra and SO(5,5) duality, JHEP 06 (2013) 095 [arXiv:1305.2258] [INSPIRE].
M. Hatsuda and W. Siegel, O(D, D) gauge fields in the T-dual string Lagrangian, JHEP 02 (2019) 010 [arXiv:1810.04761] [INSPIRE].
M. Hatsuda and W. Siegel, T-dual Superstring Lagrangian with double zweibeins, JHEP 03 (2020) 058 [arXiv:1912.05092] [INSPIRE].
M. Hatsuda and T. Kimura, Canonical approach to Courant brackets for D-branes, JHEP 06 (2012) 034 [arXiv:1203.5499] [INSPIRE].
M. Poláček and W. Siegel, Natural curvature for manifest T-duality, JHEP 01 (2014) 026 [arXiv:1308.6350] [INSPIRE].
M. Hatsuda and K. Kamimura, Classical AdS superstring mechanics, Nucl. Phys. B 611 (2001) 77 [hep-th/0106202] [INSPIRE].
E. Bergshoeff, E. Sezgin and P.K. Townsend, Supermembranes and Eleven-Dimensional Supergravity, Phys. Lett. B 189 (1987) 75 [INSPIRE].
H.-D. Feng and W. Siegel, Gauge-covariant S-matrices for field theory and strings, Phys. Rev. D 71 (2005) 106001 [hep-th/0409187] [INSPIRE].
M. Cederwall, J. Edlund and A. Karlsson, Exceptional geometry and tensor fields, JHEP 07 (2013) 028 [arXiv:1302.6736] [INSPIRE].
M. Cederwall, Twistors and supertwistors for exceptional field theory, JHEP 12 (2015) 123 [arXiv:1510.02298] [INSPIRE].
B. Julia, Group disintegrations, Conf. Proc. C 8006162 (1980) 331 [INSPIRE].
E. Cremmer and B. Julia, The N=8 Supergravity Theory. 1. The Lagrangian, Phys. Lett. B 80 (1978) 48 [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry II: Ed(d) × ℝ+ and M theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, Solution to the Ward Identities for Superamplitudes, JHEP 10 (2010) 103 [arXiv:0911.3169] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, SUSY Ward identities, Superamplitudes, and Counterterms, J. Phys. A 44 (2011) 454009 [arXiv:1012.3401] [INSPIRE].
G. Bossard et al., E9 exceptional field theory. Part I. The potential, JHEP 03 (2019) 089 [arXiv:1811.04088] [INSPIRE].
G. Bossard et al., E9 exceptional field theory. Part II. The complete dynamics, JHEP 05 (2021) 107 [arXiv:2103.12118] [INSPIRE].
W. Siegel, S-matrices from 4d worldvolume, arXiv:2012.12938 [INSPIRE].
Acknowledgments
We are grateful to Martin Roček and Yuqi Li for the fruitful discussions. We also acknowledge the Simons Center for Geometry and Physics for its hospitality during “The Simons Summer Workshop in Mathematics and Physics 2022 and 2023” where this work has been developed. W.S. is supported by NSF award PHY-19105093. M.H. is supported in part by Grant-in-Aid for Scientific Research (C), JSPS KAKENHI Grant Numbers JP22K03603 and JP20K03604.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2307.04934
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Hatsuda, M., Hulík, O., Linch, W.D. et al. \( \mathcal{A} \)-theory — A brane world-volume theory with manifest U-duality. J. High Energ. Phys. 2023, 87 (2023). https://doi.org/10.1007/JHEP10(2023)087
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2023)087