STRING STRING DUALITY CONJECTURE IN SIX DIMENSIONS AND CHARGED SOLITONIC STRINGS

TL;DR

This work tests the six-dimensional string-string duality between type IIA on K3 and heterotic on T^4 by analyzing solitonic string solutions. It shows that charged heterotic strings arise as non-singular solitons in the IIA theory via $O(d,d)$-generated deformations of the heterotic string soliton, yielding a $24$-parameter family corresponding to $20$ left-moving and $4$ right-moving worldsheet currents, with charge generated through Chern-Simons-like couplings to the antisymmetric tensor field. Conversely, the fundamental IIA string remains uncharged under Ramond-Ramond fields and does not admit a charged deformation, aligning with worldsheet current expectations. The results bolster the string-string duality in six dimensions and discuss prospects for exact conformal-field-theory descriptions of these solitons.

Abstract

It has recently been conjectured that the type IIA string theory compactified on K3 and the heterotic string theory compactified on a four dimensional torus describe identical string theories. The fundamental heterotic string can be regarded as a non-singular soliton solution of the type IIA string theory with a semi-infinite throat. We show that this solution admits 24 parameter non-singular deformation describing a fundamental heterotic string carrying electric charge and current. The charge is generated due to the coupling of the gauge fields to the anti-symmetric tensor field, and not to an explicit source term. This clarifies how soliton solutions carrying charge under the Ramond-Ramond fields can be constructed in the type IIA theory, and provides further support to the string string duality conjecture. Similarly, the fundamental type IIA string can be regarded as a non-singular solution of the heterotic string theory with a semi-infinite throat, but this solution does not admit any deformation representing charged string. This is also consistent with the expectation that a fundamental type IIA string does not carry any charge that couples to the fields originating in the Ramond-Ramond sector.