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

Sen, Ashoke

doi:10.1088/1126-6708/2008/07/078

Cited by 30 publications

(29 citation statements)

References 32 publications

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“…After splitting C k−2 and C k−2 into their finite and polar parts, and representing the latter as a Poincaré sum, we shall show that the unfolded sum over matrices A accounts for all possible splittings of a charge (Q, P ) = (Q 1 , P 1 ) + (Q 2 , P 2 ) into two 1/2-BPS constituents, labeled by A ∼ p q r s ∈ M 2 (Z) [33], (Q 1 , P 1 ) = (p, r) sQ − qP ps − qr , (Q 2 , P 2 ) = (q, s) pP − rQ ps − qr . (2.15) Generalizing the analysis in [40], we shall show that the discontinuity of Ω 6 (Γ, t) for an arbitrary primitive (but possibly torsionful) charge Γ is given by a variant of (2.12) where Ω 4 (Γ) on the right-hand side is replaced by Ω 4 (Γ) = d≥1 Γ/d ∈Λe⊕Λm Ω 4 (Γ/d) , (2.16) in agreement with the macroscopic analysis in [35].…”

Section: )supporting

confidence: 75%

“…jump in Ω 6 (Q, P ; t) can then be shown to agree [33,34,35] with the primitive wall-crossing formula [36] ∆Ω 6 (Γ) = −(−1) Γ 1 ,Γ 2 +1 Ω 4 (Γ 1 ) Ω 4 (Γ 2 ) , (2.12) where ∆Ω 6 is the index in the chamber where the bound state exists, minus the index in the chamber where it does not. The formula (2.8) only applies to dyons whose charge is primitive with unit torsion and that is generic, in the sense that it belongs to the highest stratum in the following graph of inclusions 2…”

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confidence: 83%

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Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

2019

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Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the ∇ 2 (∇φ) 4 effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one-and two-loop corrections, plus non-perturbative effects of order e −1/g 2 3 . We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results. In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact ∇ 2 F 4 effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order e −R from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order e −R 2 from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.G (24,8) ab,cd = R.N.[P ] is a genus-h Siegel-Narain theta series for a lattice of signature (p, q) with a polynomial insertion (see (B.4) and (2.32) for the genus-one and two cases), ∆ and Φ 10 are the modular discriminants in genus-one and two, and R.N. denotes a specific regularization prescription. We demonstrated that the Ansätze (1.4) and (1.5) satisfy the relevant supersymmetric Ward identities, and that their asymptotic expansion at weak heterotic string coupling g 3 → 0 reproduces the known perturbative contributions, up to one-loop and two-loop, respectively, plus an infinite series of O(e −1/g 2 3 ) corrections ascribed to NS5-instantons, Kaluza-Klein (6,1)-branes and H-monopole instantons. We went on to analyze the limit R → ∞ and demonstrated that the O(e −R ) corrections to F (24,8) abcd and to G (24,8) ab,cd were proportional to the known helicity supertraces of 1/2-and 1/4-BPS four-dimensional black holes, respectively. In particular, the DVV formula for the index of 1/4-BPS states [5], with the correct contour prescription [9], emerges in a transparent fashion after unfolding the integral over the fundamental domain Sp(4, Z)\H 2 onto the full Siegel upper-half plane H 2 .In [22], we extended the study of the 1/2-BPS saturated coupling F (24,8) abcd to the case of CHL heterotic orbifolds of prime order N = 2, 3,...

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Section: )supporting

confidence: 75%

Section: )mentioning

confidence: 83%

Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

2019

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“…In 4D case, the exact degeneracy changes as the sign of Q Á P change. This jump in the degeneracy is related to the issue of walls of marginal stability as discussed in detail in [19,20]. As pointed out below (5), there is an extra zero atṽ ¼ 0 inÈ, compared tõ È bmpv .…”

Section: Discussionmentioning

confidence: 89%

Subleading correction to statistical entropy for Breckenridge-Myers-Peet-Vafa black holes

Banerjee

2009

Phys. Rev. D

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“…For two-center solutions the latter term refers to the situation, when in moduli space after crossing walls of marginal stability the attractor flows are separately evolving to the attractor points of the constituent single center solutions. Recently these developments have triggered activity in a variety of new research fields such as attractor flow trees, entropy enigmas, microstate counting, and bound state recombination [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Two-center black holes, qubits, and elliptic curves

Lévay

2011

Phys. Rev. D

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We relate the U-duality invariants characterizing two-center extremal black-hole solutions in the stu, st 2 , and t 3 models of N ¼ 2, d ¼ 4 supergravity to the basic invariants used to characterize entanglement classes of four-qubit systems. For the elementary example of a D0D4-D2D6 composite in the t 3 model we illustrate how these entanglement invariants are related to some of the physical properties of the two-center solution. Next we show that it is possible to associate elliptic curves to charge configurations of two-center composites. The hyperdeterminant of the hypercube, a four-qubit polynomial invariant of order 24 with 2 894 276 terms, is featuring the j invariant of the elliptic curve. We present some evidence that this quantity and its straightforward generalization should play an important role in the physics of two-center solutions.

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

Cited by 30 publications

References 32 publications

Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

Subleading correction to statistical entropy for Breckenridge-Myers-Peet-Vafa black holes

Two-center black holes, qubits, and elliptic curves

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