Abstract
Abstract
There has been strong interest in the possibility that in the quantum-gravity realm momentum space might be curved, mainly focusing, especially for what concerns phenomenological implications, on the case of a de Sitter momentum space. We here take as starting point the known fact that quantum gravity coupled to matter in
2
+
1
spacetime dimensions gives rise to an effective picture characterized by a momentum space with anti-de Sitter geometry, and we point out some key properties of
2
+
1
-dimensional anti-de Sitter momentum space. We observe that it is impossible to implement all of these properties in theories with a
3
+
1
-dimensional anti-de Sitter momentum space, and we then investigate, with the aim of providing guidance to the relevant phenomenology focusing on possible modified laws of conservation of momenta, the implications of giving up, in the
3
+
1
-dimensional case, some of the properties of the
2
+
1
-dimensional case.
Funder
Ministero dell’Istruzione e del Merito
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Università degli Studi di Napoli Federico II
Fundação de Apoio à Pesquisa do Estado da Paraíba
Compagnia di San Paolo