Abstract
We study the world-sheet conformal field theories for T-folds systematically based on the Lie algebra lattices representing the momenta of strings. The fixed point condition required for the T-duality twist restricts the possible Lie algebras. When the T-duality acts as a simple chiral reflection, one is left with the four cases, A 1 , D 2r , E 7 , E 8, among the simple simply-laced algebras. From the corresponding Englert-Neveu lattices, we construct the modular invariant partition functions for the T-fold CFTs in bosonic string theory. Similar construction is possible also by using Euclidean even self-dual lattices. We then apply our formulation to the T-folds in the E 8 × E 8 heterotic string theory. Incorporating non-trivial phases for the T-duality twist, we obtain, as simple examples, a class of modular invariant partition functions parametrized by three integers. Our construction includes the cases which are not reduced to the free fermion construction.
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References
A. Dabholkar and C. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].
S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].
A. Flournoy, B. Wecht and B. Williams, Constructing nongeometric vacua in string theory, Nucl. Phys. B 706 (2005) 127 [hep-th/0404217] [INSPIRE].
C.M. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
A. Flournoy and B. Williams, Nongeometry, duality twists and the worldsheet, JHEP 01 (2006) 166 [hep-th/0511126] [INSPIRE].
S. Hellerman and J. Walcher, Worldsheet CFTs for Flat Monodrofolds, hep-th/0604191 [INSPIRE].
S. Kawai and Y. Sugawara, D-branes in T-fold conformal field theory, JHEP 02 (2008) 027 [arXiv:0709.0257] [INSPIRE].
S. Kawai and Y. Sugawara, Mirrorfolds with K3 fibrations, JHEP 02 (2008) 065 [arXiv:0711.1045] [INSPIRE].
P. Anastasopoulos, M. Bianchi, J.F. Morales and G. Pradisi, (Unoriented) T-folds with few T’s, JHEP 06 (2009) 032 [arXiv:0901.0113] [INSPIRE].
M. Bianchi, G. Pradisi, C. Timirgaziu and L. Tripodi, Heterotic T-folds with a small number of neutral moduli, JHEP 10 (2012) 089 [arXiv:1207.2665] [INSPIRE].
C. Condeescu, I. Florakis and D. Lüst, Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory, JHEP 04 (2012) 121 [arXiv:1202.6366] [INSPIRE].
C. Condeescu, I. Florakis, C. Kounnas and D. Lüst, Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT‘s, JHEP 10 (2013) 057 [arXiv:1307.0999] [INSPIRE].
Y. Satoh and Y. Sugawara, Non-geometric Backgrounds Based on Topological Interfaces, JHEP 07 (2015) 022 [arXiv:1502.05776] [INSPIRE].
H.S. Tan, T-duality Twists and Asymmetric Orbifolds, JHEP 11 (2015) 141 [arXiv:1508.04807] [INSPIRE].
Y. Satoh, Y. Sugawara and T. Wada, Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant, JHEP 02 (2016) 184 [arXiv:1512.05155] [INSPIRE].
Y. Sugawara and T. Wada, More on Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant, JHEP 08 (2016) 028 [arXiv:1605.07021] [INSPIRE].
E. Wong and I. Affleck, Tunneling in quantum wires: A Boundary conformal field theory approach, Nucl. Phys. B 417 (1994) 403 [INSPIRE].
V.B. Petkova and J.B. Zuber, Generalized twisted partition functions, Phys. Lett. B 504 (2001) 157 [hep-th/0011021] [INSPIRE].
C. Bachas, J. de Boer, R. Dijkgraaf and H. Ooguri, Permeable conformal walls and holography, JHEP 06 (2002) 027 [hep-th/0111210] [INSPIRE].
C. Bachas and I. Brunner, Fusion of conformal interfaces, JHEP 02 (2008) 085 [arXiv:0712.0076] [INSPIRE].
Y. Satoh, On supersymmetric interfaces for string theory, JHEP 03 (2012) 072 [arXiv:1112.5935] [INSPIRE].
C. Bachas, I. Brunner and D. Roggenkamp, A worldsheet extension of O(d,d:Z), JHEP 10 (2012) 039 [arXiv:1205.4647] [INSPIRE].
S. Elitzur, B. Karni, E. Rabinovici and G. Sarkissian, Defects, Super-Poincaré line bundle and Fermionic T-duality, JHEP 04 (2013) 088 [arXiv:1301.6639] [INSPIRE].
A. Dabholkar and C. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [INSPIRE].
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE].
T. Kugo and B. Zwiebach, Target space duality as a symmetry of string field theory, Prog. Theor. Phys. 87 (1992) 801 [hep-th/9201040] [INSPIRE].
J. Erler, Asymmetric orbifolds and higher level models, Nucl. Phys. B 475 (1996) 597 [hep-th/9602032] [INSPIRE].
F. Englert and A. Neveu, Nonabelian Compactification of the Interacting Bosonic String, Phys. Lett. B 163 (1985) 349 [INSPIRE].
W. Lerche, A.N. Schellekens and N.P. Warner, Lattices and Strings, Phys. Rept. 177 (1989) 1 [INSPIRE].
S. Elitzur, E. Gross, E. Rabinovici and N. Seiberg, Aspects of Bosonization in String Theory, Nucl. Phys. B 283 (1987) 413 [INSPIRE].
A. Giveon, E. Rabinovici and G. Veneziano, Duality in String Background Space, Nucl. Phys. B 322 (1989) 167 [INSPIRE].
T. Eguchi and Y. Sugawara, Non-holomorphic Modular Forms and SL(2, ℝ)/U(1) Superconformal Field Theory, JHEP 03 (2011) 107 [arXiv:1012.5721] [INSPIRE].
K. Aoki, E. D’Hoker and D.H. Phong, On the construction of asymmetric orbifold models, Nucl. Phys. B 695 (2004) 132 [hep-th/0402134] [INSPIRE].
O. King, A mass formula for unimodular lattices with no roots, Math. Comput. 72 (2003) 839, arXiv:math/0012231.
M. Blaszczyk, S. Groot Nibbelink, O. Loukas and S. Ramos-Sanchez, Non-supersymmetric heterotic model building, JHEP 10 (2014) 119 [arXiv:1407.6362] [INSPIRE].
C. Angelantonj, I. Florakis and M. Tsulaia, Universality of Gauge Thresholds in Non-Supersymmetric Heterotic Vacua, Phys. Lett. B 736 (2014) 365 [arXiv:1407.8023] [INSPIRE].
C. Angelantonj, I. Florakis and M. Tsulaia, Generalised universality of gauge thresholds in heterotic vacua with and without supersymmetry, Nucl. Phys. B 900 (2015) 170 [arXiv:1509.00027] [INSPIRE].
A.E. Faraggi, C. Kounnas and H. Partouche, Large volume SUSY breaking with a solution to the decompactification problem, Nucl. Phys. B 899 (2015) 328 [arXiv:1410.6147] [INSPIRE].
S. Abel, K.R. Dienes and E. Mavroudi, Towards a nonsupersymmetric string phenomenology, Phys. Rev. D 91 (2015) 126014 [arXiv:1502.03087] [INSPIRE].
C. Kounnas and H. Partouche, Stringy N = 1 super no-scale models, PoS (PLANCK 2015) 070 [arXiv:1511.02709] [INSPIRE].
C. Kounnas and H. Partouche, Super no-scale models in string theory, Nucl. Phys. B 913 (2016) 593 [arXiv:1607.01767] [INSPIRE].
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Satoh, Y., Sugawara, Y. Lie algebra lattices and strings on T-folds. J. High Energ. Phys. 2017, 24 (2017). https://doi.org/10.1007/JHEP02(2017)024
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DOI: https://doi.org/10.1007/JHEP02(2017)024