High U(1) charges in type IIB models and their F-theory lift
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Springer
Received: December 8, 2018 Accepted: March 22, 2019 Published: April 1, 2019
Francesco Mattia Cianci,a Dami´ an K. Mayorga Pe˜ nab and Roberto Valandroa,c,d a
Dipartimento di Fisica, Universit` a degli Studi di Trieste, Strada Costiera 11, 34151 Trieste, Italy b Departamento de F´ısica, DCI, Universidad de Guanajuato, Loma del Bosque 103, CP 37150, Le´ on, Guanajuato, M´exico c The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy d INFN — Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
E-mail: [email protected], [email protected], [email protected] Abstract: We construct models with U(1) gauge group and matter with charges up to 6, in the context of type IIB compactifications. We show explicitly that models with charges up to 4 can be derived from corresponding models in F-theory by applying the Sen weak coupling limit. We derive which type IIB models should be the limit of charge 5 and 6 Ftheory models. Explicit six dimensional type IIB models with maximal charge 5 and 6 are constructed on an algebraic K3 surface that is the double cover of CP2 . By using type IIB results we are also able to rediscover the F-theory charge 4 model in a straightforward way. Keywords: Anomalies in Field and String Theories, D-branes, Field Theories in Higher Dimensions, Superstring Vacua ArXiv ePrint: 1811.11777
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)012
JHEP04(2019)012
High U(1) charges in type IIB models and their F-theory lift
Contents 1 Introduction
2 4 4 5 7 10
3 Type IIB limit of F-theory 3.1 F-theory models with U(1) gauge group 3.2 Sen limit 3.3 Massive and massless U(1)’s 3.4 Minimal models with high charges 3.5 6D compactification and D7-brane setup
10 10 11 13 14 17
4 Charge 3 and 4 models and their F-theory lift 4.1 Type IIB models with maximal charge 3 or 4 4.2 Charge 3 type IIB model from F-theory 4.3 Charge 4 type IIB model from F-theory 4.4 Charge 4 in F-theory from a Z3 model through type IIB
20 20 22 24 25
5 Charge 5 and 6 models in type IIB 5.1 Charge 5 (II) model in type IIB 5.2 Charge 6 model in type IIB 5.3 Explicit examples with charge 5 and 6 5.4 Models with incomplete spectra beyond charge 6 5.5 Lifting type IIB models to F-theory
26 27 28 28 30 31
6 Conclusions and future directions
32
A Divisors of order 4 in s6 , sL , sR
34
B Anomaly cancelation in 6D models
34
C Matching charged loci in charge 3 (II) model
36
D Matching charged loci in charge 4 model
39
–1–
JHEP04(2019)012
2 Type IIB manifold vs. F-theory base 2.1 Double covers 2.2 Splitting divisors from matrices 2.3 Splitting divisors of higher degree 2.4 Odd divisor classes
1
Introduction
1
Models with four U(1) symmetries have been constructed from complete intersection fibers in [8]. Similarly 8D F-theory models resulting from elliptically fibered K3 compactifications have been construted in [9]. However one expects more generic charge patterns for U(1)4 models to be r
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