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Aims. We use the stellar line-of-sight velocities of Antlia B (Ant B), afaint dwarf galaxy in the NGC 3109 association, to derive constraints on thefundamental properties of scalar field dark matter (SFDM), which was originallyproposed to solve the small-scale problems faced by cold dark matter models.Methods. We used the first spectroscopic observations of Ant B, a distant (d$\sim$ 1.35 Mpc) faint dwarf ($M_\text{V} = -9.7$, $M_\star \sim8\times10^5$M$_\odot$), from MUSE-Faint, a survey of ultra-faint dwarfsconducted using the Multi Unit Spectroscopic Explorer. By measuring theline-of-sight velocities of stars in the $1'\times 1'$ field of view, weidentified 127 stars as members of Ant B, which enabled us to model its darkmatter density profile with the Jeans modelling code GravSphere. We implementeda model for SFDM into GravSphere and used this to place constraints on theself-coupling strength of this model. Results. We find a virial mass of${M_{200} \approx 1.66^{+2.51}_{-0.92}\times 10^9}$ $M_\odot$ and aconcentration parameter of ${c_{200}\approx 17.38^{+6.06}_{-4.20}}$ for Ant B.These results are consistent with the mass-concentration relations in theliterature. We constrain the characteristic length scale of the repulsiveself-interaction $R_{\text{TF}}$ of the SFDM model to $R_{\text{TF}} \lesssim180$ pc ($68\%$ confidence level), which translates to a self-coupling strengthof $\frac{g}{m^2c^4}\lesssim 5.2 \times 10^{-20}$ eV$^{-1}$cm$^3$. Theconstraint on the characteristic length scale of the repulsive self-interactionis inconsistent with the value required to match observations of the cores ofdwarf galaxies in the Local Group, suggesting that the cored density profilesof those galaxies are not caused by SFDM.

The MUSE-Faint survey. III. Constraining scalar field dark matter with Antlia B