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The deconfined quantum critical point (DQCP) is an example of phasetransitions beyond the Landau symmetry breaking paradigm that attracts wideinterest. However, its nature has not been settled after decades of study. Inthis paper, we apply the recently proposed fuzzy sphere regularization to studythe $\mathrm{SO}(5)$ non-linear sigma model (NL$\sigma$M) with a topologicalWess-Zumino-Witten term, which serves as a dual description of the DQCP with anexact $\mathrm{SO}(5)$ symmetry. We demonstrate that the fuzzy sphere functionsas a powerful microscope, magnifying and revealing a wealth of crucialinformation about the DQCP, ultimately paving the way towards its final answer.In particular, through exact diagonalization, we provide clear evidence thatthe DQCP exhibits approximate conformal symmetry. The evidence includes theexistence of a conserved $\mathrm{SO}(5)$ symmetry current, a stress tensor,and integer-spaced levels between conformal primaries and their descendants.Most remarkably, we have identified 23 primaries and 76 conformal descendants.Furthermore, by examining the renormalization group flow of the lowest symmetrysinglet as well as other primaries, we provide numerical evidence in favour ofDQCP being pseudo-critical, with the approximate conformal symmetry plausiblyemerging from nearby complex fixed points. The primary spectrum we compute alsohas important implications, including the conclusion that the $\mathrm{SO}(5)$DQCP cannot describe a direct transition from the N\'eel to valence bond solidphase on the honeycomb lattice.

The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere  Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator  Spectrum