Towards Non-archimedean Superstrings

Abstract

An action for a prospect of a $p$-adic open superstring on a target Minkowski space is proposed. The action is constructed for `worldsheet' fields taking values in the $p$-adic field ${\mathbb{Q}}_p$, but it is assumed to be obtained from a discrete action on the Bruhat-Tits tree. This action is proven to have an analog of worldsheet supersymmetry and the superspace action is also constructed in terms of superfields. The action does not have conformal symmetry, however it is implemented in the definition of the amplitudes. The tree-level amplitudes for this theory are obtained for $N$ vertex operators corresponding to tachyon superfields and a Koba-Nielsen formula is obtained. Finally, four-point amplitudes are computed explicitly and they are compared to previous work on $p$-adic superstring amplitudes.

arXiv comment26 pages, no figures

References in corpus (9)

• Large N Field Theories, String Theory and Gravity
• $p$-adic AdS/CFT
• p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field
• Signs of the time: Melonic theories over diverse number systems
• Towards p-Adic String in Constant B-Field
• Spin in $p$-adic AdS/CFT
• Meromorphic Continuation of Koba-Nielsen String Amplitudes
• The boundary theory of a spinor field theory on the Bruhat-Tits tree
• Euclidean Quantum Field Formulation of p-Adic open string amplitudes

Cited by in corpus (3)

• Finite Temperature at Finite Places
• Effective field theories on subspaces of the Bruhat-Tits tree
• The $p$-adic Jaynes-Cummings model in symplectic geometry