Two centered black holes andN= 4 dyon spectrum

Abstract

The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy of two centered small black holes which (dis)appear as we cross the walls of marginal stability.

QUANTUM ENTROPY FUNCTION FROM AdS2/CFT1 CORRESPONDENCE

“…In this case on the black hole side the contribution to the entropy is known to come solely from single centered black holes with a single AdS 2 factor in their near horizon geometry. On the other hand as we cross a wall of marginal stability new multi-centered solutions carrying the same total charge and mass appear, and d micro ( q) in such a background should count the total degeneracies of single and multi-centered black holes [56,57,58,59,60,61,7,62,63,64]. Since our analysis has been based on the partition function of a single AdS 2 , it is only natural that Z AdS 2 will only contain information about single centered black holes.…”

Wall Crossing, Discrete Attractor Flow and Borcherds Algebra

“…Firstly, it was known from the start that the dyon-counting formula proposed in [6] is related to the denominator formula of a Borcherds-Kac-Moody superalgebra [7,8]. Secondly, thanks to the simplification brought by higher supersymmetries, the moduli-dependence of the BPS states in the N = 4, d = 4 theories has been extensively studied in the last two years [9,10,11,12,13,14]. In this paper we will see how the two aspects of the N = 4, d = 4 dyon spectrum are intimately related to each other.…”

Wall crossing formula for 𝒩 = 4 dyons: a macroscopic derivation

“…Such subspaces are known as walls of marginal stability, and the jump in the index across these walls -known as the wall crossing formula -has been the subject of intense investigation in recent years [4,5,6,7,8,9,10,11,12]. While most of the work has been focussed on half-BPS dyonic black holes in N = 2 supersymmetric string theories, by now we also have a good understanding of this phenomenon in N = 4 and N = 8 supersymmetric string theories [13,14,15,16,17,18,19,20]. In fact in the latter theories the situation is somewhat better since we also have a good understanding of the exact spectrum of BPS dyons in these theories.…”