| Summary: | Abstract We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED3) coupled to N f flavors of two-component Dirac fermions. We show the lattice and perturbative results on the SO(5) symmetric DQCP are excluded by the bootstrap bounds with an assumption that the lowest singlet scalar is irrelevant. Remarkably, we discover a new family of kinks in the 3D SO(N) vector bootstrap bounds with N ⩾ 6. We demonstrate coincidences between SU(N f ) adjoint and SO N f 2 − 1 $$ \textrm{SO}\left({N}_f^2-1\right) $$ vector bootstrap bounds due to a novel algebraic relation between the crossing equations. By introducing gap assumptions breaking the SO N f 2 − 1 $$ \textrm{SO}\left({N}_f^2-1\right) $$ symmetry, the SU(N f ) adjoint bootstrap bounds with large N f converge to the 1/N f perturbative results of QED3. Our results provide strong evidence that the SO(5) DQCP is not continuous and the critical flavor number of QED3 is slightly above 2: N f ∗ ∈ 2 4 $$ {N}_f^{\ast}\in \left(2,4\right) $$ . Bootstrap results near N f ∗ $$ {N}_f^{\ast } $$ are well consistent with the merger and annihilation mechanism for the loss of conformality in QED3.
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