Counting all dyons in N =4 string theory

Understand

For dyons in heterotic string theory compactified on a six-torus, with electric charge vector Q and magnetic charge vector P, the positive integer I = g.c.d.(Q \wedge P) is an invariant of the U-duality group.

• We propose the microscopic theory for computing the spectrum of all dyons for all values of I, generalizing earlier results that exist only for the simplest case of I=1.
• Our derivation uses a combination of arguments from duality, 4d-5d lift, and a careful analysis of fermionic zero modes.
• The resulting degeneracy agrees with the black hole degeneracy for large charges and with the degeneracy of field-theory dyons for small charges.