We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Octonionic Magical Supergravity, Niemeier Lattices, and Exceptional & Hilbert Modular Forms.
- Authors
Günaydin, Murat; Kidambi, Abhiram
- Abstract
The quantum degeneracies of Bogomolny‐Prasad‐Sommerfield (BPS) black holes of octonionic magical supergravity in five dimensions are studied. Quantum degeneracy is defined purely number theoretically as the number of distinct states in charge space with a given set of invariant labels. Quantum degeneracies of spherically symmetric stationary BPS black holes are given by the Fourier coefficients of modular forms of exceptional group E7(−25)$E_{7(-25)}$. Their charges take values in the lattice defined by the exceptional Jordan algebra over integral octonions. The quantum degeneracies of rank 1 and rank 2 BPS black holes are given by the Fourier coefficients of singular modular forms E4(Z)$E_4(Z)$ and E8(Z)$E_8(Z)$. The rank 3 (large) BPS black holes will be studied elsewhere. Following the work of N. Elkies and B. Gross on embeddings of cubic rings A into the exceptional Jordan algebra we show that the quantum degeneracies of rank 1 black holes described by such embeddings are given by the Fourier coefficients of the Hilbert modular forms (HMFs) of SL(2,A)$SL(2,A)$. If the discriminant of the cubic ring A is D=p2$D=p^2$ with p a prime number then the isotropic lines in the 24 dimensional orthogonal complement of A define a pair of Niemeier lattices which can be taken as charge lattices of some BPS black holes. The current status of the searches for the M/superstring theoretic origins of the octonionic magical supergravity is also reviewed.
- Subjects
MODULAR forms; BLACK holes; PRIME numbers; INVARIANT sets; SUPERGRAVITY; SPACE charge; LATTICE theory
- Publication
Fortschritte der Physik / Progress of Physics, 2024, Vol 72, Issue 2, p1
- ISSN
0015-8208
- Publication type
Article
- DOI
10.1002/prop.202300242