Bridgeland stability condition

In mathematics, and especially algebraic geometry, a Bridgeland stability condition, defined by Tom Bridgeland, is an algebro-geometric stability condition defined on elements of a triangulated category. The case of original interest and particular importance is when this triangulated category is the derived category of coherent sheaves on a Calabi–Yau manifold, and this situation has fundamental links to string theory and the study of D-branes.

Such stability conditions were introduced in a rudimentary form by Michael Douglas called ${\displaystyle \Pi }$-stability and used to study BPS B-branes in string theory.^[1] This concept was made precise by Bridgeland, who phrased these stability conditions categorically, and initiated their study mathematically.^[2]