Type II chiral affine Lie algebras and string actions in doubled space. (English) Zbl 1388.81183
Summary: We present affine Lie algebras generated by the supercovariant derivatives and the supersymmetry generators for the left and right moving modes in the doubled space. Chirality is manifest in our doubled space as well as the T-duality symmetry. We present gauge invariant bosonic and superstring actions preserving the two-dimensional diffeomorphism invariance and the \(\kappa\)-symmetry where doubled spacetime coordinates are chiral fields. The doubled space becomes the usual space by dimensional reduction constraints.
MSC:
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
Keywords:
supersymmetry and duality; superstrings and heterotic strings; space-time symmetries; string dualityReferences:
| [1] | W. Siegel, Covariant approach to superstrings, in Symposium on anomalies, geometry, topology, Chicago U.S.A. (1985), W.A. Bardeen and A.R. White eds., World Scientific, Singapore (1985), pg. 348. |
| [2] | W. Siegel, Covariant superstrings, in Unified string theories, Santa Barbara U.S.A. (1985), M. Green and D. Gross eds., World Scientific, Singapore (1985), pg. 559. · Zbl 0652.58044 |
| [3] | W. Siegel, Classical Superstring Mechanics, Nucl. Phys.B 263 (1986) 93 [INSPIRE]. · doi:10.1016/0550-3213(86)90029-5 |
| [4] | W. Siegel, Randomizing the superstring, Phys. Rev.D 50 (1994) 2799 [hep-th/9403144] [INSPIRE]. |
| [5] | M.J. Duff, Duality Rotations in String Theory, Nucl. Phys.B 335 (1990) 610 [INSPIRE]. · Zbl 0967.81519 · doi:10.1016/0550-3213(90)90520-N |
| [6] | A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett.B 242 (1990) 163 [INSPIRE]. · doi:10.1016/0370-2693(90)91454-J |
| [7] | A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys.B 350 (1991) 395 [INSPIRE]. · doi:10.1016/0550-3213(91)90266-Z |
| [8] | J. Maharana and J.H. Schwarz, Noncompact symmetries in string theory, Nucl. Phys.B 390 (1993) 3 [hep-th/9207016] [INSPIRE]. · doi:10.1016/0550-3213(93)90387-5 |
| [9] | W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev.D 47 (1993) 5453 [hep-th/9302036] [INSPIRE]. |
| [10] | W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev.D 48 (1993) 2826 [hep-th/9305073] [INSPIRE]. |
| [11] | W. Siegel, Manifest duality in low-energy superstrings, hep-th/9308133 [INSPIRE]. · Zbl 0844.58101 |
| [12] | N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math.54 (2003) 281 [math/0209099] [INSPIRE]. · Zbl 1076.32019 |
| [13] | M. Gualtieri, Generalized complex geometry, math/0401221. · Zbl 1235.32020 |
| [14] | C.M. Hull, A Geometry for non-geometric string backgrounds, JHEP10 (2005) 065 [hep-th/0406102] [INSPIRE]. · doi:10.1088/1126-6708/2005/10/065 |
| [15] | C.M. Hull, Doubled Geometry and T-Folds, JHEP07 (2007) 080 [hep-th/0605149] [INSPIRE]. · doi:10.1088/1126-6708/2007/07/080 |
| [16] | C.M. Hull, Generalised Geometry for M-theory, JHEP07 (2007) 079 [hep-th/0701203] [INSPIRE]. · doi:10.1088/1126-6708/2007/07/079 |
| [17] | M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept.423 (2006) 91 [hep-th/0509003] [INSPIRE]. · doi:10.1016/j.physrep.2005.10.008 |
| [18] | C. Hull and B. Zwiebach, Double Field Theory, JHEP09 (2009) 099 [arXiv:0904.4664] [INSPIRE]. · doi:10.1088/1126-6708/2009/09/099 |
| [19] | O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP08 (2010) 008 [arXiv:1006.4823] [INSPIRE]. · Zbl 1291.81255 · doi:10.1007/JHEP08(2010)008 |
| [20] | O. Hohm, S.K. Kwak and B. Zwiebach, Unification of Type II Strings and T-duality, Phys. Rev. Lett.107 (2011) 171603 [arXiv:1106.5452] [INSPIRE]. · doi:10.1103/PhysRevLett.107.171603 |
| [21] | I. Jeon, K. Lee and J.-H. Park, Ramond-Ramond Cohomology and O(D,D) T-duality, JHEP09 (2012) 079 [arXiv:1206.3478] [INSPIRE]. · Zbl 1397.81261 · doi:10.1007/JHEP09(2012)079 |
| [22] | I. Jeon, K. Lee, J.-H. Park and Y. Suh, Stringy Unification of Type IIA and IIB Supergravities under N = 2 D = 10 Supersymmetric Double Field Theory, Phys. Lett.B 723 (2013) 245 [arXiv:1210.5078] [INSPIRE]. · Zbl 1311.83062 · doi:10.1016/j.physletb.2013.05.016 |
| [23] | R. Blumenhagen, F. Hassler and D. Lüst, Double Field Theory on Group Manifolds, JHEP02 (2015) 001 [arXiv:1410.6374] [INSPIRE]. · Zbl 1388.81401 · doi:10.1007/JHEP02(2015)001 |
| [24] | G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav.30 (2013) 163001 [arXiv:1305.1907] [INSPIRE]. · Zbl 1273.83001 · doi:10.1088/0264-9381/30/16/163001 |
| [25] | O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys.61 (2013) 926 [arXiv:1309.2977] [INSPIRE]. · Zbl 1338.81328 · doi:10.1002/prop.201300024 |
| [26] | M. Hatsuda, K. Kamimura and W. Siegel, Superspace with manifest T-duality from type-II superstring, JHEP06 (2014) 039 [arXiv:1403.3887] [INSPIRE]. · doi:10.1007/JHEP06(2014)039 |
| [27] | M. Poláček and W. Siegel, T-duality off shell in 3D Type II superspace, JHEP06 (2014) 107 [arXiv:1403.6904] [INSPIRE]. · doi:10.1007/JHEP06(2014)107 |
| [28] | M. Hatsuda, K. Kamimura and W. Siegel, Ramond-Ramond gauge fields in superspace with manifest T-duality, JHEP02 (2015) 134 [arXiv:1411.2206] [INSPIRE]. · Zbl 1388.83819 · doi:10.1007/JHEP02(2015)134 |
| [29] | E. Witten, Nonabelian Bosonization in Two-Dimensions, Commun. Math. Phys.92 (1984) 455 [INSPIRE]. · Zbl 0536.58012 · doi:10.1007/BF01215276 |
| [30] | M. Hatsuda and K. Kamimura, Classical AdS superstring mechanics, Nucl. Phys.B 611 (2001) 77 [hep-th/0106202] [INSPIRE]. · Zbl 0971.83068 · doi:10.1016/S0550-3213(01)00338-8 |
| [31] | M. Hatsuda, Sugawara form for AdS superstring, Nucl. Phys.B 730 (2005) 364 [hep-th/0507047] [INSPIRE]. · Zbl 1206.83144 · doi:10.1016/j.nuclphysb.2005.10.001 |
| [32] | W. Siegel, Manifest Lorentz Invariance Sometimes Requires Nonlinearity, Nucl. Phys.B 238 (1984) 307 [INSPIRE]. · doi:10.1016/0550-3213(84)90453-X |
| [33] | E. Cremmer, B. Julia, H. Lü and C.N. Pope, Dualization of dualities. 2. Twisted self-duality of doubled fields and superdualities, Nucl. Phys.B 535 (1998) 242 [hep-th/9806106] [INSPIRE]. · Zbl 1080.81598 · doi:10.1016/S0550-3213(98)00552-5 |
| [34] | S.F. Hassan, SO(d, d) transformations of Ramond-Ramond fields and space-time spinors, Nucl. Phys.B 583 (2000) 431 [hep-th/9912236] [INSPIRE]. · Zbl 0984.81117 · doi:10.1016/S0550-3213(00)00337-0 |
| [35] | W. Siegel, New superspaces/algebras for superparticles/strings, arXiv:1106.1585 [INSPIRE]. |
| [36] | M. Poláček and W. Siegel, Natural curvature for manifest T-duality, JHEP01 (2014) 026 [arXiv:1308.6350] [INSPIRE]. · Zbl 1333.83200 · doi:10.1007/JHEP01(2014)026 |
| [37] | S. Bonanos, J. Gomis, K. Kamimura and J. Lukierski, Maxwell Superalgebra and Superparticle in Constant Gauge Badkgrounds, Phys. Rev. Lett.104 (2010) 090401 [arXiv:0911.5072] [INSPIRE]. · doi:10.1103/PhysRevLett.104.090401 |
| [38] | M. Hatsuda and T. Kimura, Canonical approach to Courant brackets for D-branes, JHEP06 (2012) 034 [arXiv:1203.5499] [INSPIRE]. · Zbl 1397.81253 · doi:10.1007/JHEP06(2012)034 |
| [39] | M. Sakaguchi, Type II superstrings and new space-time superalgebras, Phys. Rev.D 59 (1999) 046007 [hep-th/9809113] [INSPIRE]. |
| [40] | M. Sakaguchi, (p, q)-strings and new space-time superalgebras, JHEP02 (1999) 017 [hep-th/9811143] [INSPIRE]. · Zbl 0965.81084 |
| [41] | M. Abe, M. Hatsuda, K. Kamimura and T. Tokunaga, SO(2, 1) covariant IIB superalgebra, Nucl. Phys.B 553 (1999) 305 [hep-th/9903234] [INSPIRE]. · Zbl 0958.81129 · doi:10.1016/S0550-3213(99)00306-5 |
| [42] | W.D. Linch and W. Siegel, F-theory Superspace, arXiv:1501.02761 [INSPIRE]. |
| [43] | W.D. Linch, III and W. Siegel, F-theory from Fundamental Five-branes, arXiv:1502.00510 [INSPIRE]. · Zbl 1460.83102 |
| [44] | W.D. Linch and W. Siegel, F-theory with Worldvolume Sectioning, arXiv:1503.00940 [INSPIRE]. · Zbl 1462.81159 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
