Non-supersymmetric vacua and self-adjoint extensions

• Published in: The journal of high energy physics Vol. 2023; no. 8; pp. 41 - 44
• Main Authors: Mourad, J., Sagnotti, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 09.08.2023; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Boundary conditions; Classical and Quantum Gravitation; Eigenvalues; Elementary Particles; Field Theories in Higher Dimensions; General Relativity and Quantum Cosmology; Gravitons; High energy physics; High Energy Physics - Phenomenology; High Energy Physics - Theory; Intervals; Mathematical Physics; Minkowski space; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Singularity (mathematics); String Theory; Superstring Vacua; Supersymmetry; Supersymmetry Breaking; Tensors; Superstring Vacua; Field Theories in Higher Dimensions; Supersymmetry Breaking; boundary condition; tadpole; space, Minkowski; graviton, massless; spectrum, scalar; string, compactification; space-time, Minkowski; pole; anti-de Sitter; gravitation; conformal; singularity; orientifold, vacuum state; supersymmetry, symmetry breaking; stability; dimension, 9
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP08(2023)041

A bstract Internal intervals spanned by finite ranges of a conformal coordinate z and terminating at a pair of singularities are a common feature of many string compactifications with broken supersymmetry. The squared masses emerging in lower-dimensional Minkowski spaces are then eigenvalues of Schrödinger-like operators, whose potentials have double poles at the ends of the intervals. For one-component systems, the possible self-adjoint extensions of Schrödinger operators are described by points in AdS 3 × S 1 , and those corresponding to independent boundary conditions at the ends of the intervals by points on the boundary of AdS 3 . The perturbative stability of compactifications to Minkowski space time depends, in general, on these choices of self-adjoint extensions. We apply this setup to the orientifold vacua driven by the “tadpole potential” V = T e 3 2 ϕ and find, in nine dimensions, a massive scalar spectrum, a unique choice of boundary conditions with stable tensor modes and a massless graviton, and a wide range of choices leading to massless and/or massive vector modes.