Adding charges toN= 4 dyons

Abstract

The spectrum of dyons in a class of N=4 supersymmetric string theories has been found for a specific set of electric and magnetic charge vectors. We extend the analysis to more general charge vectors by considering various charge carrying collective excitations of the original system.

Two centered black holes andN= 4 dyon spectrum

“…The precise sign convention used for defining these charges can be found in [13]. We shall denote by M the symmetric SO(2, 2) matrix that encodes information about the moduli labelling the torus S 1 × S 1 and by a + iS the axion-dilaton modulus.…”

“…We now have a good understanding of the exact spectrum of a class of quarter BPS dyons in N = 4 supersymmetric string theories, obtained by taking an asymmetric Z Z N orbifold of heterotic or type IIA string theory compactified on T 6 [1][2][3][4][5][6][7][8][9][10][11][12][13]. It is also known that as we cross various walls of marginal stability associated with the possible decay of the dyon into a pair of half BPS states, the degeneracy changes by a certain amount that is exactly computable [11].…”

𝒩 = 8 dyon partition function and walls of marginal stability

“…The S-duality invariance of Ψ allows us to calculate the jump in the index across a wall of marginal stability by calculating the residue at the pole(s) the contour crosses as we deform it from the initial position to the final position calculated according to (1.11). It follows from the corresponding analysis in N = 4 supersymmetric string theories [13,19,20] that as we cross a wall of marginal stability associated with the decay into a pair of half-BPS states 15) the contour crosses the pole atρ…”

Threel string junction and 𝒩 = 4 dyon spectrum

“…We now have a good understanding of the exact spectrum of a class of quarter BPS dyons in a variety of N = 4 supersymmetric string theories [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Since by going to the appropriate region in the moduli space of these string theories and taking a decoupling limit we can recover N = 4 supersymmetric gauge theories [19,20], the spectrum of quarter BPS dyons in N = 4 supersymmetric string theories provides us information about the spectrum of quarter BPS dyons in N = 4 supersymmetric gauge theories.…”

“…Thus in heterotic string theory on T 4 × T 2 , the charge vectors carried by this state will be (β, −α) = (Q 0 , P 0 ) with Q 0 , P 0 given in (15).…”