Logarithmic Conformal Field Theories and Strings in Changing Backgrounds

TL;DR

This paper explores the application of Logarithmic Conformal Field Theory to string theory in dynamic backgrounds, focusing on D-brane recoil and the effects of supersymmetry on quantum non-linearity.

Contribution

It highlights the role of logarithmic vertex operators in non-conformal deformations and discusses how supersymmetry influences the linearity of quantum mechanics in string theory.

Findings

Recoil logarithmic vertex operators act as non-conformal deformations.

World-sheet supersymmetry suppresses non-linear quantum effects.

Liouville dressing is necessary for certain background deformations.

Abstract

I review a particular class of physical applications of Logarithmic Conformal Field Theory in strings propagating in changing (not necessarily conformal) backgrounds, namely D-brane recoil in flat or time-dependent cosmological backgrounds. The role of recoil logarithmic vertex operators as non-conformal deformations, requiring in some cases Liouville dressing, is pointed out. It is also argued that, although in the case of non-supersymmetric recoil deformations the representation of target time as a Liouville zero mode may lead to non-linear quantum mechanics for stringy defects, such non-linearities disappear (or, at least, are strongly suppressed) after world-sheet supersymmetrization. A possible link is therefore suggested between (world-sheet) supersymmetry and linearity of quantum mechanics in this framework.