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SUMMARY: A 2D-CFT Factory: Critical Lattice Models Derived from generalise
 d symmetries - Ling Yan (Janet) Hung\, Tsinghua University
DTSTART:20251030T130000Z
DTEND:20251030T140000Z
UID:TALK234886@talks.cam.ac.uk
CONTACT:122734
DESCRIPTION:In this talk\, we introduce a ``CFT factory'' : a novel algori
 thm of methodically generating 2D lattice models that would flow to 2D con
 formal fixed points in the infrared. These 2D models are realised by givin
 g critical boundary conditions to 3D TQFT\, described by string-net models
 \, often called the strange correlators. We engineer these critical bounda
 ry conditions by harnessing the non-commutativity of generators of general
 ised non-invertible symmetries\, realised as anyons in the 3D TQFT. The no
 n-invertible symmetries preserved at the critical point can be controlled 
 by studying a novel ``refined condensation tree''.  Our structured method 
 generates an infinite family of critical lattice models\, including the A-
 series minimal models\, and uncovers previously unknown critical points. N
 otably\, we find at least three novel critical points (c≈1.3\, 1.8\, and
  2.5 respectively) preserving the Haagerup symmetries\, in addition to rec
 overing previously reported ones. The condensation tree\, together with a 
 generalised Kramers-Wannier duality\, predicts precisely large swathes of 
 phase boundaries\, fixes almost completely the global phase diagram\, and 
 sieves out second order phase transitions. This is not only illustrated in
  well-known examples (such as the 8-vertex model related to the A5 categor
 y) but also further verified with precision numerics\, using our improved 
 (non-invertible) symmetry-preserving tensor-network RG\, in novel examples
  involving the Haagerup symmetries. We show that critical couplings can be
  precisely encoded in the categorical data (Frobenius algebras and quantum
  dimensions in unitary fusion categories)\, thus establishing a powerful\,
  systematic route to discovering and potentially classifying new conformal
  field theories.  
LOCATION:Potter room
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