Jan Manschot

AdS 3 partition functions reconstructed

For pure gravity in AdS3, Witten has given a recipe for the construction of holomorphically factorizable partition functions of pure gravity theories with central charge c = 24k. The partition function was found to be a polynomial in the modular invariant j-function. We show that the partition function can be obtained instead as a modular sum which has a more physical interpretation as a sum over geometries. We express both the j-function and its derivative in terms of such a sum.

The chiral ring of AdS3/CFT2 and the attractor mechanism

We study the moduli dependence of the chiral ring in N = (4, 4) superconformal field theories, with special emphasis on those CFTs that are dual to type IIB string theory on AdS(3) x S-3 x X-4. The chiral primary operators are sections of vector bundles, whose connection describes the operator mixing under motion on the moduli space. This connection can be exactly computed using the constraints from N = (4, 4) supersymmetry. Its curvature can be determined using the tt* equations, for which we give a derivation in the physical theory which does not rely on the topological twisting. We show that for N = (4, 4) theories the chiral ring is covariantly constant over the moduli space, a fact which can be seen as a non-renormalization theorem for the three-point functions of chiral primaries in AdS(3)/CFT2. From the spacetime point of view our analysis has the following applications. First, in the case of a D1/D5 black string, we can see the matching of the attractor flow in supergravity to RG-flow in the boundary field theory perturbed by irrelevant operators, to first order away from the fixed point. Second, under spectral flow the chiral primaries become the Ramond ground states of the CFT. These ground states represent the microstates of a small black hole in five dimensions consisting of a D1/D5 bound state. The connection that we compute can be considered as an example of Berrys phase for the internal microstates of a supersymmetric black hole.

From black holes to quivers

A bstractMiddle cohomology states on the Higgs branch of supersymmetric quiver quantum mechanics — also known as pure Higgs states — have recently emerged as possible microscopic candidates for single-centered black hole micro-states, as they carry zero angular momentum and appear to be robust under wall-crossing. Using the connection between quiver quantum mechanics on the Coulomb branch and the quantum mechanics of multi-centered black holes, we propose a general algorithm for reconstructing the full moduli-dependent cohomology of the moduli space of an arbitrary quiver, in terms of the BPS invariants of the pure Higgs states. We analyze many examples of quivers with loops, including all cyclic Abelian quivers and several examples with two loops or non-Abelian gauge groups, and provide supporting evidence for this proposal. We also develop methods to count pure Higgs states directly.

The Chiral ring of AdS(3)/CFT(2) and the attractor mechanism

We study the moduli dependence of the chiral ring in N = (4, 4) superconformal field theories, with special emphasis on those CFTs that are dual to type IIB string theory on AdS(3) x S-3 x X-4. The chiral primary operators are sections of vector bundles, whose connection describes the operator mixing under motion on the moduli space. This connection can be exactly computed using the constraints from N = (4, 4) supersymmetry. Its curvature can be determined using the tt* equations, for which we give a derivation in the physical theory which does not rely on the topological twisting. We show that for N = (4, 4) theories the chiral ring is covariantly constant over the moduli space, a fact which can be seen as a non-renormalization theorem for the three-point functions of chiral primaries in AdS(3)/CFT2. From the spacetime point of view our analysis has the following applications. First, in the case of a D1/D5 black string, we can see the matching of the attractor flow in supergravity to RG-flow in the boundary field theory perturbed by irrelevant operators, to first order away from the fixed point. Second, under spectral flow the chiral primaries become the Ramond ground states of the CFT. These ground states represent the microstates of a small black hole in five dimensions consisting of a D1/D5 bound state. The connection that we compute can be considered as an example of Berrys phase for the internal microstates of a supersymmetric black hole.

D3-instantons, mock theta series and twistors

A bstractThe D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,

On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants

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Reducing the critical switching current in nanoscale spin valves

). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2,

The Coulomb Branch Formula for Quiver Moduli Spaces

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Nonmonotonic angular magnetoresistance in asymmetric spin valves

) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.

Generalized quiver mutations and single-centered indices

A bstractIn previous work we have shown that the equivariant index of multi-centered