**Speaker: **Linhao Li (ISSP, U Tokyo)

**Title: ** Boundary conditions and LSM anomalies of conformal field

theories in 1+1 dimensions

**Abstract:** In this talk, we will study a relationship between

conformally invariant boundary conditions and anomalies of conformal

field theories (CFTs) in 1+1 dimensions. For a given CFT with a global

symmetry, we consider symmetric gapping potentials which are relevant

perturbations to the CFT. If a gapping potential is introduced only in

a subregion of the system, it provides a certain boundary condition to

the CFT. From this equivalence, if there exists a Cardy boundary state

which is invariant under a symmetry, then the CFT can be gapped with a

unique ground state by adding the corresponding gapping potential.

This means that the symmetry of the CFT is anomaly free. Using this

approach, we will systematically deduce the anomaly-free conditions

for various types of CFTs with several different symmetries. When the

symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis

type ingappability of the system. Our results are consistent with,

where available, known results in the literature. Moreover, we extend

the discussion to other symmetries including spin groups and

generalized time-reversal symmetries. As an application, we propose 1d

LSM theorem involving magnetic space group symmetries on the lattice.

The extended LSM theorems apply to systems with a broader class of

spin interactions, such as Dzyaloshinskii-Moriya interactions and

chiral three-spin interactions.