Noninvertible Chiral Symmetry and Exponential Hierarchies
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Engineering topics
Ohmori, Kantaro
Publications and source records attributed to Ohmori, Kantaro.
Generalized symmetry breaking scales and weak gravity conjectures
We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the magnetic and axion versions of the weak gravity conjecture can be motivated by the assumption that generalized global symmetries should be strongly broken within the context of low-energy effective field theory, i.e. at a characteristic scale less than the Planck scale where quantum gravity effects become important. For example, the assumption that the electric one-form symmetry of Maxwell theory should be strongly broken below the Planck scale implies the weak gravity conjecture. Similarly, the violation of generalized non-invertible symmetries is closely tied to analogs of this conjecture for non-abelian gauge theory. This reasoning enables us to unify these conjectures with the absence of global symmetries in quantum gravity.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Numerical Evidence for a Haagerup Conformal Field Theory
We numerically study an anyon chain based on the Haagerup fusion category and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is ~2. Fusion categories generalize the concept of finite group symmetries to noninvertible symmetry operations, and the Haagerup fusion category is the simplest one which comes from neither finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries. Basically the same result was independently obtained in the preceding Letter [Phys. Rev. Lett. 128, 231602 (2022)].
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Decorated Z 2 symmetry defects and their time-reversal anomalies
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
We formulate a family of spin Topological Quantum Field Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf–Witten TQFTs. They are obtained by gauging G-equivariant invertible spin-TQFTs, or, in physics language, gauging the interacting fermionic Symmetry Protected Topological states (SPTs) with a finite group G symmetry. We use the fact that the torsion part of the classification is given by Pontryagin duals to spin-bordism groups of the classifying space BG. We also consider unoriented analogues, that is G-equivariant invertible pin ± -TQFTs (fermionic time-reversal-SPTs) and their gauging. We compute these groups for various examples of abelian G using Adams spectral sequence and describe all corresponding TQFTs via certain bordism invariants in 3, 4 and other dimensions. This gives explicit formulas for the partition functions of spin-TQFTs on closed manifolds with possible extended operators inserted. The results also provide explicit classification of ’t Hooft anomalies of fermionic QFTs with finite abelian group symmetries in one dimension lower. We construct new anomalous boundary spin-TQFTs (surface fermionic topological orders). Finally, we explore SPT and symmetry enriched topologically (SET) ordered states, and crystalline SPTs protected by space-group (e.g. translation Z) or point-group (e.g. reflection, inversion or rotation C m ) symmetries, via the layer-stacking construction.
97 MATHEMATICS AND COMPUTING↗
Exceptional Chern-Simons-Matter dualities
We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is ( E N ) 1 ↔ S U ( 9 - N ) - 1 . Others such as S O ( 3 ) 8 ↔ P S U ( 3 ) - 6 , are dualities among theories with classical gauge groups that arise dueto their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons-matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant G 2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Sigma models on flags
We study (1+1)-dimensional non-linear sigma models whose target space is the flag manifold U(N)\over U(N_1)\times U(N_2)\cdots U(N_m) , with a specific focus on the special case U(N)/U(1)^{N} U ( N ) / U ( 1 ) N . These generalize the well-known \mathbb{CP}^{N-1} ℂ ℙ N − 1 model. The general flag model exhibits several new elements that are not present in the special case of the \mathbb{CP}^{N-1} ℂ ℙ N − 1 model. It depends on more parameters, its global symmetry can be larger, and its ’t Hooft anomalies can be more subtle. Our discussion based on symmetry and anomaly suggests that for certain choices of the integers N_I N I and for specific values of the parameters the model is gapless in the IR and is described by an SU(N)_1 S U ( N ) 1 WZW model. Some of the techniques we present can also be applied to other cases.
Ohmori, Kantaro↗