Two-dimensional supergravities and matrix model holography

• Applicant: Dr. Franz Ciceri, Ph.D.
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 521509185

Supergravity theories are supersymmetric extensions of general relativity, which describe the low-energy effective dynamics of string theories. The latter are of central importance for modern theoretical physics research, since they stand as prominent candidates for a consistent description of quantum gravity. While remarkable progress were made over the last decades towards the understanding of string theories properties, their unified formulation, known as M-theory, remains elusive. My research project focuses on the study of models resulting from dimensional compactifications of supergravity theories to two spacetime dimensions. Many such models are still “terra incognita” and are of particular interest in the context of the gauge/gravity duality. I will indeed argue that the analysis of their vacuum structure will, using holographic techniques, shed light on some of the properties of M-theory. Upon toroidal compactifications to two spacetime dimensions, supergravity theories exhibit infinite-dimensional rigid symmetries based on affine Kac-Moody algebras. The corresponding models have been extensively studied and consist of integrable non-linear sigma models coupled to dilaton gravity. The most interesting example is that of the maximally supersymmetric model, for which the rigid symmetry group E9 is the affine extension of the exceptional Lie group E8. As in higher-dimensions, deformations of this model can be obtained by gauging certain non-abelian subgroups of the rigid symmetry group. The resulting maximal gauged supergravities, which also emerge from flux compactifications on curved backgrounds, typically possess interesting anti de Sitter vacua that play a central role for holography. In two dimensions however, a complete construction of the gauged supergravities dynamics has long been missing, and in particular, the expression of their scalar potentials was unknown. The vacuum landscapes of these gauged supergravities therefore remain uncharted territory. By studying a large class of two-dimensional flux compactifications, and using techniques based on exceptional geometry, I was recently able to complete the construction of the gauged dynamics. The goal of my research project is to analyze specific gaugings for which the theory admits two-dimensional anti de Sitter vacua, and to holographically study the properties of the dual matrix models. I will in particular focus on the maximally supersymmetric two-dimensional SO(9) gauged supergravity, which follows from the consistent truncation of type IIA supergravity on the eight-sphere. This theory admits an SO(9)-invariant anti de Sitter vacuum, whose uplift to ten dimensions describes the near-horizon geometry of N interacting D0-branes. This is especially interesting since the holographically dual field theory is the supersymmetric SU(N) matrix quantum mechanics, known as the BFSS matrix model, which itself has been proposed as a non-perturbative definition of M-theory.

• DFG Programme: WBP Fellowship
• International Connection: France
• Host: Professor Dr. Henning Samtleben