On field redefinitions and exact solutions in string theory

TL;DR

The paper demonstrates a covariant field redefinition linking exact and leading-order string backgrounds, revealing scheme-dependent solutions and the persistent influence of $lpha'$ corrections on probes like tachyons.

Contribution

It introduces a local covariant lpha'-dependent field redefinition connecting exact and approximate string backgrounds, clarifying scheme dependence and correction effects.

Findings

Existence of a covariant lpha'-dependent field redefinition.

Scheme in which the lpha'-corrected background is an exact solution.

Tachyon equations retain lpha' corrections, affecting probe dynamics.

Abstract

String backgrounds associated with gauged $G/H$ WZNW models in general depend non-trivially on $\alpha'$. We note, however, that there exists a local covariant $\a'$-dependent field redefinition that relates the exact metric-dilaton background corresponding to the $SL(2,R)/U(1)$ model to its leading-order form ($D=2$ black hole). As a consequence, there exists a `scheme' in which the string effective equations have the latter as an exact solution. However, the corresponding equation for the tachyon (which, like other Weyl anomaly coefficients, has scheme-dependent form) still contains corrections of all orders in $\alpha'$. As a result, the `probes' (the tachyons) still feel the $\alpha'$-corrected background. The field redefinitions we discuss contain the dilaton terms in the metric transformation law. We comment on exact forms of the duality transformation in different `schemes'.