The dressing method as non linear superposition in sigma models

Abstract

We apply the dressing method on the Non Linear Sigma Model (NLSM), which describes the propagation of strings on ℝ × S2, for an arbitrary seed. We obtain a formal solution of the corresponding auxiliary system, which is expressed in terms of the solutions of the NLSM that have the same Pohlmeyer counterpart as the seed. Accordingly, we show that the dressing method can be applied without solving any differential equations. In this context a superposition principle emerges: the dressed solution is expressed as a non-linear superposition of the seed with solutions of the NLSM with the same Pohlmeyer counterpart as the seed.

Novel aspects of integrability for NLSMs in symmetric spaces

“…These conclusions present a novel aspect of NLSMs integrability, which expands the framework built in the 1970s and later on. As the derivation of [100] is model specific, the generalization of these conclusions could be questionable and the structure of the superposition obscure.…”

A New 2 + 1-Dimensional Integrable Variable Coefficient Toda Equation

“…The dressing method as nonlinear superposition in Sigma models has been researched by Dimitrios Katsinis et al in ref. [14]. Multi-lump solutions of KP equation with integrable boundary are discussed in ref.…”

Entanglement entropy and gravity

“…The dressing method is exactly the implementation of this non-linear superposition rule. This Part of the dissertation is based on the publications [2][3][4][5]9,10]. It is organized as follows.…”

“…Various techniques can be used to explore the AdS/CFT correspondence at this particular limit, mainly on the side of the boundary field theory [36]. In [10] we obtain the formal solution of the auxiliary system, which corresponds to strings propagating in R × S 2 . Generalization of this construction to the supercoset P SU (2, 2|4)/SO(1, 5) × SO (6) could contribute towards establishing a direct relation between specific string configurations and dual operators.…”

“…Μπορούν να αξιοποιηθούν αρκετές τεχνικές προκειμένου να μελετηθεί η αντιστοιχία AdS/CFT σε αυτό το όριο, κυρίως από την πλευρά της θεωρίας πεδίου [36]. Στην εργασία [10] βρίσκουμε της λύση του βοηθητικού συστήματος, του αντιστοιχεί στην διάδοση χορδών στον χώρο R × S 2 . Η γενίκευση αυτής της κατασκευής στον χώρο υπερ-πηλίκο P SU (2, 2|4)/SO(1, 5) × SO (6) θα μπορούσε να συνεισφέρει στην κατεύθυνση της άμεσης συσχέτισης κλασσικών λύσεων της θεωρίας χορδών και δυϊκών τελεστών.…”