# Symmetries of the Standard Model: exact, anomalous, spontaneously brok

1. Jul 20, 2014

### Murtuza Tipu

There are a number of possible symmetries in fundamental physics, such as:

Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and Lorentz invariance proper),

conformal invariance (i.e., scale invariance, invariance by homotheties),

global and local gauge invariance, for the various gauge groups involved in the Standard Model (SU2×U1 and SU3),

flavor invariance for leptons and quarks, which can be chirally divided into a left-handed and a right-handed part ((SU3)L×(SU3)R×(U1)L×(U1)L),

discrete C, P and T symmetries.

Each of these symmetries can be

an exact symmetry,

anomalous, i.e., classically valid but broken by renormalization at the quantum level (or equivalently, if I understand correctly(?), classically valid only perturbatively but spoiled by a nonperturbative effect like an instanton),

spontaneously broken, i.e., valid for the theory but not for the vacuum state,

explicitly broken.

Also, the answer can depend on the sector under consideration (QCD, electroweak, or if it makes sense, simply QED), and can depend on a particular limit (e.g., quark masses tending to zero) or vacuum phase. Finally, each continuous symmetry should give rise to a conserved current (or an anomaly in the would-be-conserved current if the symmetry is anomalous). This makes a lot of combinations.

So here is my question: is there somewhere a systematic summary of the status of each of these symmetries for each sector of the standard model? (i.e., a systematic table indicating, for every combination of symmetry and subtheory, whether the symmetry holds exactly, is spoiled by anomaly or is spontaneously broken, with a short discussion).

The answer to each particular question can be tracked down in the literature, but I think having a common document summarizing everything in a systematic way would be tremendously useful.