Abstract
We showed that there is no SU(2) Witten anomaly in a large class of 4d \( \mathcal{N} \) = 2 supersymmetric Heterotic string compactifications. The consistency conditions we consider are the modularity of the new supersymmetric index, the integrality of BPS indices, and the discrete Peccei-Quinn shift symmetries. We also found an example where these conditions are not sufficient to show that the theory is anomaly free. This suggests that there are more conditions in the worldsheet SCFT essential for consistent string compactifications.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.N. Schellekens and N.P. Warner, Anomalies, Characters and Strings, Nucl. Phys. B 287 (1987) 317 [INSPIRE].
W. Lerche, A.N. Schellekens and N.P. Warner, Lattices and Strings, Phys. Rept. 177 (1989) 1 [INSPIRE].
M.B. Green, J.A. Harvey and G.W. Moore, I-brane inflow and anomalous couplings on D-branes, Class. Quant. Grav. 14 (1997) 47 [hep-th/9605033] [INSPIRE].
M.R. Douglas, Branes within branes, NATO Sci. Ser. C 520 (1999) 267 [hep-th/9512077] [INSPIRE].
Y.-K.E. Cheung and Z. Yin, Anomalies, branes, and currents, Nucl. Phys. B 517 (1998) 69 [hep-th/9710206] [INSPIRE].
R. Minasian and G.W. Moore, K theory and Ramond-Ramond charge, JHEP 11 (1997) 002 [hep-th/9710230] [INSPIRE].
E. Witten, An SU(2) Anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].
T. Banks, L.J. Dixon, D. Friedan and E.J. Martinec, Phenomenology and Conformal Field Theory Or Can String Theory Predict the Weak Mixing Angle?, Nucl. Phys. B 299 (1988) 613 [INSPIRE].
T. Banks and L.J. Dixon, Constraints on String Vacua with Space-Time Supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].
J. Lauer, D. Lüst and S. Theisen, Supersymmetric String Theories, Superconformal Algebras and Exceptional Groups, Nucl. Phys. B 309 (1988) 771 [INSPIRE].
I. Antoniadis, S. Ferrara, E. Gava, K.S. Narain and T.R. Taylor, Perturbative prepotential and monodromies in N = 2 heterotic superstring, Nucl. Phys. B 447 (1995) 35 [hep-th/9504034] [INSPIRE].
J.A. Harvey and G.W. Moore, Algebras, BPS states, and strings, Nucl. Phys. B 463 (1996) 315 [hep-th/9510182] [INSPIRE].
I. Antoniadis and H. Partouche, Exact monodromy group of \( \mathcal{N} \) = 2 heterotic superstring, Nucl. Phys. B 460 (1996) 470 [hep-th/9509009] [INSPIRE].
Y. Enoki and T. Watari, Modular forms as classification invariants of 4D \( \mathcal{N} \) = 2 Heterotic-IIA dual vacua, JHEP 06 (2020) 021 [arXiv:1911.09934] [INSPIRE].
I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, N = 2 type-II heterotic duality and higher derivative F terms, Nucl. Phys. B 455 (1995) 109 [hep-th/9507115] [INSPIRE].
G. Lopes Cardoso, G. Curio and D. Lüst, Perturbative couplings and modular forms in N = 2 string models with a Wilson line, Nucl. Phys. B 491 (1997) 147 [hep-th/9608154] [INSPIRE].
S. Stieberger, (0, 2) heterotic gauge couplings and their M-theory origin, Nucl. Phys. B 541 (1999) 109 [hep-th/9807124] [INSPIRE].
R. Borcherds, The Gros-Kohnen-Zagier theorem in higher dimensions, Duke Math. J. 97 (1999) 219 [alg-geom/9710002].
S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, AMS/IP Stud. Adv. Math. 1 (1996) 545 [hep-th/9406055] [INSPIRE].
A. Ceresole, R. D’Auria, S. Ferrara and A. Van Proeyen, Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity, Nucl. Phys. B 444 (1995) 92 [hep-th/9502072] [INSPIRE].
B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, Perturbative couplings of vector multiplets in N = 2 heterotic string vacua, Nucl. Phys. B 451 (1995) 53 [hep-th/9504006] [INSPIRE].
I. Brunner, M.R. Douglas, A.E. Lawrence and C. Romelsberger, D-branes on the quintic, JHEP 08 (2000) 015 [hep-th/9906200] [INSPIRE].
V. Kaplunovsky and J. Louis, On Gauge couplings in string theory, Nucl. Phys. B 444 (1995) 191 [hep-th/9502077] [INSPIRE].
P.S. Aspinwall and J. Louis, On the ubiquity of K 3 fibrations in string duality, Phys. Lett. B 369 (1996) 233 [hep-th/9510234] [INSPIRE].
D.-E. Diaconescu and C. Romelsberger, D-branes and bundles on elliptic fibrations, Nucl. Phys. B 574 (2000) 245 [hep-th/9910172] [INSPIRE].
C.T. Wall, Classification problems in differential topology V. On certain 6-manifolds, Invent. Math. 1 (1966) 355.
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories, AMS/IP Stud. Adv. Math. 1 (1996) 655 [hep-th/9302103] [INSPIRE].
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
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: 2005.01069
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
Enoki, Y., Sato, Y. & Watari, T. Witten anomaly in 4d heterotic compactificaitons with \( \mathcal{N} \) = 2 supersymmetry. J. High Energ. Phys. 2020, 180 (2020). https://doi.org/10.1007/JHEP07(2020)180
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)180