Large D-instanton effects in string theory

Abstract

By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order $\exp (-|Q|/g_s)$ to certain protected couplings in the three-dimensional effective action, but the number of distinct instantons is expected to be equal (or comparable) to the number of black hole micro-states, i.e. of order $\exp (Q^2)$. The same phenomenon also occurs for certain protected couplings in four dimensions, such as the hypermultiplet metric in type II string theories compactified on a Calabi-Yau threefold. In either case, the D-instanton series is therefore asymptotic, much like the perturbative expansion in any quantum field theory. By using a Borel-type resummation method, adapted to the Gaussian growth of the D-instanton series, we find that the total D-instanton sum has an inherent ambiguity of order $\exp (-1/g_s^2)$. We further suggest that this ambiguity can be lifted by including Kaluza-Klein monopole or NS5-brane instantons.

11 pages, uses JHEP3.cls, v2, typos fixed and added footnote, v3, minor corrections

References in corpus (23)

• Dirichlet-Branes and Ramond-Ramond Charges
• N=2 Extremal Black Holes
• Renormalons
• Black Hole Entropy in M-Theory
• Macroscopic Entropy of $N=2$ Extremal Black Holes
• Effects of D-instantons
• Counting Dyons in N=4 String Theory
• Combinatorics of Boundaries in String Theory
• A Farey Tail for Attractor Black Holes
• D-Brane Bound States Redux
• Black hole partition functions and duality
• Witten Index and Threshold Bound States of D-Branes
• Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry
• D-instantons and twistors
• Twistors and Black Holes
• Quantum Attractor Flows
• Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• D-instanton partition functions
• Gauge theory, topological strings, and S-duality
• Summing Over World-Sheet Boundaries

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• Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence
• Quantum mirror symmetry and twistors
• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Self-dual Einstein Spaces, Heavenly Metrics and Twistors
• D-instanton Induced Superpotential
• $R^3$ index for four-dimensional $N=2$ field theories
• S-duality in Twistor Space
• On the topology of the hypermultiplet moduli space in type II/CY string vacua
• Dualities and fivebrane instantons
• Hypermultiplet metric and D-instantons
• Fivebrane instantons in Calabi-Yau compactifications
• TBA for non-perturbative moduli spaces
• Universality of the topological string at large radius and NS-brane resurgence
• Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Heterotic-Type II duality in the hypermultiplet sector
• A case study about the mass exclusion limits for the BSM vector resonances with the direct couplings to the third quark generation
• Quantum TBA for refined BPS indices