1 Correction to: Ann. Henri Poincaré https://doi.org/10.1007/s00023-020-00988-0

Equation (5.20),

$$\begin{aligned} S_{BV}= & {} \int _{T[1]\Sigma } \!\!\!\! d^2 \sigma d^2 \theta \, \left[ \varvec{{A}}_i \, \varvec{\mathrm {d}}{x}^i + \tfrac{1}{2} \pi ^{ij}({x})\, \varvec{{A}}_i \varvec{{A}}_{j} \right] + \int _{T[1]N} \!\!\!\! d^3 \sigma d^3 \theta \, H({x}) \\&+ \int _{T[1]\Sigma } \!\!\!\! d^2 \sigma d^2 \theta \, \left[ \tfrac{1}{4} (\pi ^{il} \pi ^{jm} H_{lmk})({x}) \, \varvec{{A}}_i \varvec{{A}}_j \varvec{\varepsilon } {x}^k - \tfrac{1}{2} (\pi ^{il} H_{jkl}) ({x})\, \varvec{{A}}_i (\varvec{\mathrm {d}}{x}^j) \varvec{\varepsilon } {x}^k \right] \\&+ \int _{T[1]\Sigma } \!\!\!\! d^2 \sigma d^2 \theta \, \left[ \tfrac{1}{8} (\pi ^{im} \pi ^{jn} \pi ^{pq} H_{mql}H_{npk})({x})\, \varvec{{A}}_i \varvec{{A}}_j (\varvec{\varepsilon } {x}^k) \varvec{\varepsilon } {x}^l \right] , \end{aligned}$$

should read as follows:

$$\begin{aligned} S_{BV}= & {} \int _{T[1]\Sigma } \!\!\!\! d^2 \sigma d^2 \theta \, \left[ \varvec{{A}}_i \, \varvec{\mathrm {d}}{x}^i + \tfrac{1}{2} \pi ^{ij}({x})\, \varvec{{A}}_i \varvec{{A}}_{j} \right] + \int _{T[1]N} \!\!\!\! d^3 \sigma d^3 \theta \, H({x}) \\&+ \int _{T[1]\Sigma } \!\!\!\! d^2 \sigma d^2 \theta \, \left[ \tfrac{1}{4} (\pi ^{il} \pi ^{jm} H_{lmk})({x}) \, \varvec{{A}}_i \varvec{{A}}_j \varvec{\varepsilon } {x}^k + \tfrac{1}{2} (\pi ^{il} H_{jkl}) ({x})\, \varvec{{A}}_i (\varvec{\mathrm {d}}{x}^j) \varvec{\varepsilon } {x}^k \right] \\&+ \int _{T[1]\Sigma } \!\!\!\! d^2 \sigma d^2 \theta \, \left[ \tfrac{1}{8} (\pi ^{im} \pi ^{jn} \pi ^{pq} H_{mql}H_{npk})({x})\, \varvec{{A}}_i \varvec{{A}}_j (\varvec{\varepsilon } {x}^k) \varvec{\varepsilon } {x}^l \right] . \end{aligned}$$