Exact noncommutative solitons in p-adic strings and BSFT

TL;DR

This paper constructs exact noncommutative solitons in p-adic string theory and boundary string field theory, showing their persistence across all noncommutative parameters and their smooth interpolation between different regimes.

Contribution

It introduces exact noncommutative solitons in p-adic and boundary string field theories, demonstrating their existence for all noncommutative parameters, unlike in usual scalar theories.

Findings

Noncommutative solitons exist for all theta values.

Solitons interpolate smoothly between p-adic and noncommutative regimes.

Solitons persist below a critical theta, unlike in standard scalar theories.

Abstract

The tachyon field of p-adic string theory is made noncommutative by replacing ordinary products with noncommutative products in its exact effective action. The same is done for the boundary string field theory, treated as the p -> 1 limit of the p-adic string. Solitonic lumps corresponding to D-branes are obtained for all values of the noncommutative parameter theta. This is in contrast to usual scalar field theories in which the noncommutative solitons do not persist below a critical value of theta. As theta varies from zero to infinity, the solution interpolates smoothly between the soliton of the p-adic theory (respectively BSFT) to the noncommutative soliton.