dS spaces and brane worlds in exotic string theories
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Springer
Received: March 24, 2020 Accepted: May 24, 2020 Published: June 10, 2020
Ralph Blumenhagen,a Max Brinkmann,a Andriana Makridou,a,b Lorenz Schlechtera and Matthias Traubea a
Max-Planck-Institut f¨ ur Physik (Werner-Heisenberg-Institut), F¨ ohringer Ring 6, 80805 M¨ unchen, Germany b Fakult¨ at f¨ ur Physik, Ludwig-Maximilians-Universit¨ at M¨ unchen, Theresienstr. 37, 80333 M¨ unchen, Germany
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We investigate string-phenomenological questions of Hull’s exotic superstring theories with Euclidean strings/branes and multiple times. These are known to be plagued by pathologies like the occurrence of ghosts. On the other hand, these theories exhibit de Sitter solutions. Our special focus lies on the question of the coexistence of such de Sitter solutions and ghost-free brane worlds. To this end, the world-sheet CFT description of Euclidean fundamental strings is generalized to include also the open string/D-brane sector. Demanding that in the “observable” gauge theory sector the gauge fields themselves are non-ghosts, a generalization of the dS swampland conjecture is found. Keywords: Conformal Field Models in String Theory, D-branes, Superstrings and Heterotic Strings ArXiv ePrint: 2002.11746
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)077
JHEP06(2020)077
dS spaces and brane worlds in exotic string theories
Contents 1 Introduction
1 4 4 6 10
3 Ghosts in exotic string theories 3.1 Ghosts for the Lorentzian string 3.2 Ghosts for the Euclidean string 3.3 Speculations and objectives
12 13 16 18
4 CFT description of Euclidean exotic strings 4.1 Basics of CFTs with Euclidean world-sheets 4.2 Boundary states 4.3 Fermionic boundary states 4.4 The influence of space-time signature 4.5 Orientifolds of Euclidean strings
19 19 24 26 29 31
5 D-branes for exotic string theories 5.1 D-branes for Euclidean exotic strings 5.2 Ghost-free D-brane theories 5.3 Orientifolds of Lorentzian exotic strings
33 33 37 38
6 Conclusions
42
A (A)dS spaces of signature (p, q)
43
B Table of branes in exotic IIB theories
44
C Table of branes in exotic IIA theories
45
1
Introduction
Even though it is believed that there exists a huge landscape of string compactifications, it turns out to be notoriously difficult to realize certain four-dimensional properties. This led to the idea of the swampland [1] which contains those low-energy effective theories that cannot be UV completed to a consistent theory of quantum gravity. The swampland program intends to extract a set of relatively simple quantitative features that low-energy
–1–
JHEP06(2020)077
2 Preliminaries 2.1 Fluxed AdS ×dS solutions 2.2 Exotic superstring theories 2.3 Map of type II action to exotic actions
1
On the same note, in [31, 32] the authors argued that time dependent backgrounds might circumvent the dS swampland conjecture. 2 Questions concerning the backreaction of spherical Euclidean
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