DAI-FREED ANOMALIES IN PARTICLE PHYSICS Miguel Montero ITF, Utrecht - PowerPoint PPT Presentation

DAI-FREED ANOMALIES IN PARTICLE PHYSICS Miguel Montero ITF, Utrecht University 
 (Work in collaboration with Iñaki García-Etxebarria) Stringpheno 2018


 
 
 QUICK RECAP Iñaki just explained the Dai- Freed formalism to compute anomalies of fermion systems in d Y dimensions. X Anomalies cancel if exp(2 π i η Y ) is independent of the choice of Y 
 Y 1 Y 2 X To ensure this, we must have exp(2 π i η Y )=1 on any allowed (d+1) manifold.

Dai-Freed anomalies have only been studied in a few systems.

Dai-Freed anomalies have only been studied in a few systems. A priori, any gauge theory could be Dai-Freed anomalous!

Dai-Freed anomalies have only been studied in a few systems. A priori, any gauge theory could be Dai-Freed anomalous! This talk: Apply Dai-Freed to symmetries of interest in particle physics .

Dai-Freed anomalies have only been studied in a few systems. A priori, any gauge theory could be Dai-Freed anomalous! This talk: Apply Dai-Freed to symmetries of interest in particle physics . Is the Standard Model Dai-Freed anomalous?

PLAN OF THE TALK Discrete symmetries Strategy Proton triality 
 Connection to Ibañez-Ross The SM as a Anomalies of semisimple topological Lie groups superconductor GUT’s Spin Z 4 structure SM and MSSM MSSM story

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 Once local anomalies cancel, η is a bordism invariant: 
 exp(2 π i η Y 1 ) = exp(2 π i η Y 2 ) Y 1 Y 2 Bordism is an equivalence relation, which defines bordism groups 
 Ω Spin d +1 ( BG ) These classify (d+1)-dimensional manifolds, with a principal G-bundle, modulo bordism (bundle extends over bordism too) Computed using AHSS . η is a group homomorphism from the relevant bord. group to U(1).

GENERAL STRATEGY Compute relevant bordism group If it vanishes, there is no new anomaly. Y, compute η . Find a nontrivial manifold If it vanishes, there is no new anomaly. If η is nonvanishing, there is an anomaly.

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