Bootstrapping conformal QED3 and deconfined quantum critical point
Zhijin Li
Abstract
A bstract We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED 3 ) 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 $$ \textrm{SO}\left({N}_f^2-1\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>SO</mml:mi> <mml:mfenced> <mml:mrow> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> vector bootstrap bounds due to a novel algebraic relation between the crossing equations. By introducing gap assumptions breaking the $$ \textrm{SO}\left({N}_f^2-1\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>SO</mml:mi> <mml:mfenced> <mml:mrow> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> symmetry, the SU( N f ) adjoint bootstrap bounds with large N f converge to the 1/ N f perturbative results of QED 3 . Our results provide strong evidence that the SO(5) DQCP is not continuous and the critical flavor number of QED 3 is slightly above 2: $$ {N}_f^{\ast}\in \left(2,4\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>f</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mo>∈</mml:mo> <mml:mfenced> <mml:mn>2</mml:mn> <mml:mn>4</mml:mn> </mml:mfenced> </mml:math> . Bootstrap results near $$ {N}_f^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>f</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> are well consistent with the merger and annihilation mechanism for the loss of conformality in QED 3 .