BPS spectrum, wall crossing and quantum dilogarithm identity

Understand

BPS spectrum with finite number of states are found for higher rank four dimensional N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a Riemann surface with various kinds of defects.

• The wall crossing formula is interpreted as the quantum dilogarithm identity.
• Various methods including quiver representation theory, maximal green mutation, and cluster algebra are used extensively.
• The spectral generator and its refined version for the higher rank theory are written down using the explicit spectrum information.