Strings from Nambu-Goto to Polyakov and back

Abstract: I discuss the recent progress in bypassing the KPZ barrier for the existence of nonperturbative bosonic strings in $1<d<25$. I consider string anomalies which emerge from higher terms of the DeWitt-Seeley expansion as $\varepsilon \times \varepsilon^{-1}$ with $\varepsilon$ being a UV cutoff. I show they give a nonvanishing contribution to the central charge and to the string susceptibility, telling the Nambu-Goto and Polyakov strings apart. I describe an exact solution of the emerging four-derivative two-dimensional conformal theory and its relation to minimal models. Talk at "Gravity, Strings and Fields: A Conference in Honour of Gordon Semenoff", Montreal July 24-28, 2023.