Dyon spectrum in Script N = 4 supersymmetric type II string theories

Abstract

We compute the spectrum of quarter BPS dyons in freely acting Z Z 2 and Z Z 3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula agrees with the corresponding black hole entropy to first non-leading order after taking into account corrections due to the curvature squared terms in the effective action. The result is significant since in these theories the entropy of a small black hole, computed using the curvature squared corrections to the effective action, fails to reproduce the statistical entropy associated with elementary string states.1

Heat kernels on the AdS2 cone and logarithmic corrections to extremal black hole entropy

“…where 9) and E ℓ = ℓ (ℓ + 1). By using standard trigonometric identities one can reduce this to the form…”

“…This program has been very explicitly carried out for a class of supersymmetric black holes and a detailed matching of the string answer has been done in the large charge limit, where the string answer explicitly matches with the Bekenstein-Hawking, or more generally, the Wald entropy [2] of the black hole in question [3][4][5][6][7][8][9][10]. We refer the reader to [11] for a review and a more exhaustive set of references.…”

𝒩 = 8 dyon partition function and walls of marginal stability

“…The analysis proceeds exactly parallel to that for N = 4 supersymmetric string theories described in [9,10,11,18]. We consider type IIB string theory compactified on a six dimensional torus denoted as T 4 × S 1 × S 1 and consider in this theory a 1/8 BPS configuration consisting of a Kaluza-Klein (KK)…”

Adding charges toN= 4 dyons

“…We can switch on flux of world-volume gauge field strengths F on the D5-brane along the various 2-cycles of K3 that it wraps. The net coupling of the RR gauge fields to the D5-brane in the presence of the world-volume gauge fields may be expressed as [14] 8) up to a constant of proportionality. The integral is over the D5-brane world-volume spanned by y, t and the coordinates of K3.…”