BPS spectrum, wall crossing and quantum dilogarithm identity

Abstract

BPS spectrum with finite number of states are found for higher rank four dimensional N = 2 theory engineered from six dimensional AN-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. The finite chamber has an interesting N3 behavior in the large N limit.