Towards p-Adic String in Constant B-Field

TL;DR

This paper explores how adding a B-field background to p-adic string theory affects the spacetime properties of the tachyon, revealing connections to noncommutative geometry and extending the theoretical framework.

Contribution

It introduces a new term in the p-adic string action representing a B-field background and analyzes its implications for noncommutative deformations of the tachyon's effective theory.

Findings

The B-field term can be incorporated into the p-adic string action.

The B-field induces a noncommutative deformation of the tachyon's spacetime theory.

The results suggest a link between p-adic string theory and noncommutative geometry.

Abstract

Spacetime properties of the tachyon of the p-adic string theory can be derived from a (non-local) action on the p-adic line Q_p, thought of as the boundary of the `worldsheet'. We show that a term corresponding to the background of the antisymmetric second rank tensor field B can be added to this action. We examine the consequences of this term, in particular, its relation to a noncommutative deformation of the effective theory of the p-adic tachyon in spacetime.