Projects per year
Abstract
In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown nontrivial conformal field theories (CFTs). Here we investigate the extent to which this is possible in the case where the global symmetry group has a product structure. We do this by testing for signatures of fixed points using a mixedcorrelator bootstrap calculation with a minimal set of input assumptions. This ‘semiblind’ approach contrasts with other approaches for probing more complicated groups, which ‘target’ known theories with additional spectral assumptions or use the saturation of the singlecorrelator bootstrap bound as a starting point. As a case study, we select the space of CFTs with productgroup symmetry O(15) ⊗ O(3) in d = 3 dimensions. On the assumption that there is only one relevant scalar (ℓ = 0) singlet operator in the theory, we find a single ‘allowed’ region in our chosen space of scaling dimensions. The scaling dimensions corresponding to two known largeN critical theories, the Heisenberg and the chiral ones, lie on or very near the boundary of this region. The largeN antichiral point lies well outside the ‘allowed’ region, which is consistent with the expectation that the antichiral theory is unstable, and thus has an additional relevant scalar singlet operator. We also find a sharp kink in the boundary of the ‘allowed’ region at values of the scaling dimensions that do not correspond to the (N, M ) = (3, 15) instance of any largeN predicted O(N ) ⊗ O(M ) critical theory.
Original language  English 

Article number  147 
Number of pages  27 
Journal  Journal of High Energy Physics 
Volume  2021 
Issue number  3 
DOIs  
Publication status  Published  15 Mar 2021 
Keywords
 Conformal and W symmetry
 Conformal field theory
 Global symmetries
Fingerprint
Dive into the research topics of 'Multifixed point numerical conformal bootstrap: a case study with structured global symmetry'. Together they form a unique fingerprint.Projects
 1 Finished

Controlling Emergent Orders in Quantum: Controlling Emergent Orders in Quantum Materials
Wahl, P., Hooley, C. & Lee, S.
1/06/18 → 30/06/23
Project: Standard