Instanton Strings and HyperKaehler Geometry

Abstract

We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N=(4,4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS_3. We derive a precise map relating the moduli of the K3 type IIB string compactification to the moduli of these conformal field theories and the corresponding classical hyperkaehler geometry. We conclude that, in the absense of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyperkaehler manifolds.

latex, 33 pages

Cited by in corpus (113)

• Large N Field Theories, String Theory and Gravity
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• D-brane Charges in Five-brane backgrounds
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• The quantum structure of black holes
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• D1-D5-P microstates at the cap
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• Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
• Deforming the D1D5 CFT away from the orbifold point
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• Matching of correlators in AdS_3/CFT_2
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• TsT, $T\bar{T}$ and black strings
• The Search for a Holographic Dual to AdS(3)xS(3)xS(3)xS(1)
• Exciting AdS Orbifolds
• Excitations in the deformed D1D5 CFT
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• Exact N=4 correlators of AdS(3)/CFT(2)
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• Comments on the $S_N$ orbifold CFT in the large $N$-limit
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• Full action of two deformation operators in the D1D5 CFT
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• The Stranger Things of Symmetric Product Orbifold CFTs
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• One-Loop Transition Amplitudes in the D1D5 CFT
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• D1D5 System and Noncommutative Geometry
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