Supersymmetric protection and the Swampland
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Springer
Received: April 8, 2020 Accepted: June 9, 2020 Published: June 26, 2020
Supersymmetric protection and the Swampland
a
Max-Planck-Institut f¨ ur Physik (Werner-Heisenberg-Institut), 80805 M¨ unchen, Germany b Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel c Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, U.S.A. d PRISMA Cluster of Excellence and Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universit¨ at, 55099 Mainz, Germany
E-mail: [email protected], [email protected], [email protected] Abstract: For certain terms in the action, supersymmetry can forbid an infinite number of possible contributions. We study whether such protection can occur in quantum gravity even without sufficient supersymmetry. We focus on whether the superpotential can vanish exactly in four-dimensional N = 1 theories, and if the prepotential can be exactly cubic in N = 2 theories. We investigate these questions in string theory and find that for almost all known string constructions the corrections allowed by supersymmetry do occur. However, we do find some special settings where all the corrections can be proven to vanish. These examples all share the common feature that they are related, through a certain orbifolding by a discrete gauged R-symmetry element, to a higher supersymmetric theory. Motivated by these results, we propose a Swampland criterion that any theory which enjoys such protection beyond its realised supersymmetry must have a direct connection to a higher supersymmetric theory. Keywords: F-Theory, Nonperturbative Effects, Superstring Vacua, Supersymmetric Effective Theories ArXiv ePrint: 2003.10452
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)168
JHEP06(2020)168
Eran Palti,a,b Cumrun Vafac and Timo Weigandd
Contents 1 Introduction
2 5 5 7 8 9 12 13 13 14
3 String compactifications with extra protection 3.1 N = 1 theories 3.1.1 F-theory vacua with torsional discriminant 3.1.2 IIB orbifold vacua with Z2 fixed points 3.2 N = 2 theories 3.2.1 Type II string theory on orbifolds 3.2.2 IIA string theory on the Enriques Calabi-Yau
15 15 16 18 23 23 24
4 Characteristics of the examples with extra protection
25
5 Discussion
26
A Flux lifting of D3-instanton zero-modes in F-theory A.1 General mechanism A.2 No flux lifting for B3 = P1 × P2
28 28 28
B Stringy heterotic instantons
31
C Superpotentials in heterotic compactifications C.1 Standard embeddings C.2 Non-standard embeddings
32 34 36
D Type IIA, Type I and M-theory vacua
37
–1–
JHEP06(2020)168
2 String compactifications with generic corrections 2.1 F-theory vacua with N = 1 supersymmetry 2.1.1 Instantons on generic Calabi-Yau fourfolds 2.1.2 Deformation zero mode lifting by instanton flux 2.1.3 Deformation zero mode lifting by D3 brane interactions 2.1.4 χ(Y4 ) = 0 manifolds 2.1.5 The E8 superpotential 2.2 Other N = 1 string vacua 2.3 N = 2 prepotentials and their corrections
1
Introduction
N = 1 supersymmetry. In N
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