Rigid limit for hypermultiplets and five-dimensional gauge theories

Alexandrov, Sergei; Banerjee, Sibasish; Longhi, Pietro

doi:10.1007/jhep01(2018)156

Cited by 18 publications

(21 citation statements)

References 82 publications

(209 reference statements)

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“…In this approach the metric is encoded in the complex contact structure on the twistor space, a CP 1 -bundle over M H . The D-instanton corrected contact structure has been constructed to all orders in the instanton expansion in [32,35], and an explicit expression for the metric has been derived recently in [54,55]. Here we will present only those elements of the construction which are relevant for the subsequent analysis, and refer to reviews [56,57] for more details.…”

Section: H and Twistorial Description Of Instantonsmentioning

confidence: 99%

Black Holes and Higher Depth Mock Modular Forms

Alexandrov

Pioline

2019

Commun. Math. Phys.

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By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi-Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4-D2-D0 black holes in type IIA string theory compactified on the same space. Mathematically, these BPS degeneracies are the generalized Donaldson-Thomas invariants counting coherent sheaves with support on a divisor D, at the large volume attractor point. For D irreducible, this function is closely related to the elliptic genus of the superconformal field theory obtained by wrapping M5-brane on D and is therefore known to be modular. Instead, when D is the sum of n irreducible divisors D i , we show that the generating function acquires a modular anomaly. We characterize this anomaly for arbitrary n by providing an explicit expression for a non-holomorphic modular completion in terms of generalized error functions. As a result, the generating function turns out to be a (mixed) mock modular form of depth n − 1. BPS indices and wall-crossingIn this section, we review some aspects of BPS indices in theories with N = 2 supersymmetry, including the tree flow formula relating the moduli-dependent index Ω(γ, z a ) to the attractor index Ω ⋆ (γ). We then apply this formalism in the context of Calabi-Yau string vacua, and express the generalized DT invariants Ω(γ, z a ) in terms of their counterparts evaluated at the large volume attractor point (1.1), known as MSW invariants. Wall-crossing and attractor flowsThe BPS index Ω(γ, z a ) counts (with sign) micro-states of BPS black holes with total electromagnetic charge γ = (p Λ , q Λ ), for a given value z a of the moduli at spatial infinity. While Ω(γ, z a ) is a locally constant function over the moduli space, it can jump across real codimension one loci where certain bound states, represented by multi-centered black hole solutions of N = 2 supergravity, become unstable. The positions of these loci, known as walls of marginal stability, are determined by the central charge Z γ (z a ), a complex-valued linear function of γ whose modulus gives the mass of a BPS state of charge γ, while the phase determines the supersymmetry subalgebra preserved by the state. Since a bound state can only decay when its mass becomes equal to the sum of masses of its constituents, it is apparent that the walls correspond to hypersurfaces where the phases of two central charges, say Z γ L (z a ) and Z γ R (z a ), become aligned. The bound states which may become unstable are then those whose constituents have charges in the positive cone spanned by γ L and γ R . We shall assume that the charges γ L , γ R have non-zero Dirac-Schwinger-Zwanziger (DSZ) pairing γ L , γ R = 0, since otherwise marginal bound states may form, whose stability is hard to control.The general relation between the values of Ω(γ, z a ) on the two sides of a wall has been found in the mathematics literature by and Joyce-Song [42,43], and justified physically in a series of works [6,7,8,9]. However, in this work we require a somewhat differe...

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Section: H and Twistorial Description Of Instantonsmentioning

confidence: 99%

Black Holes and Higher Depth Mock Modular Forms

Alexandrov

Pioline

2019

Commun. Math. Phys.

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“…We expect that these questions may be appropriately approached through our framework. Another application of computing such BPS spectra would be the study of D-instanton corrections to metrics on hypermultiplet moduli spaces of type II string theory [79][80][81]. 29 Soliton data in field theory: kinky vortices Another pressing question that was postponed throughout this work regards the physical interpretation of the soliton data in the nonabelianization map.…”

Section: More Calabi-yausmentioning

confidence: 99%

Exploring 5d BPS Spectra with Exponential Networks

Banerjee

Longhi

Romo

2019

Ann. Henri Poincaré

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We develop geometric techniques for counting BPS states in five-dimensional gauge theories engineered by M theory on a toric Calabi-Yau threefold. The problem is approached by studying framed 3d-5d wall-crossing in presence of a single M5 brane wrapping a special Lagrangian submanifold L. The spectrum of 3d-5d BPS states is encoded by the geometry of the manifold of vacua of the 3d-5d system, which further coincides with the mirror curve describing moduli of the Lagrangian brane. The information about the BPS spectrum is extracted from the geometry of the mirror curve by construction of a nonabelianization map for the exponential networks. For the simplest Calabi-Yau, C 3 we reproduce the count of 5d BPS states encoded by the Mac Mahon function in the context of topological strings, and match predictions of 3d tt * geometry for the count of 3d-5d BPS states. We comment on applications of our construction to the study of enumerative invariants of toric Calabi-Yau threefolds.

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“…Since the original relativistic fluid is at rest, the kinematical "inverse-velocity" variable potentially present in the Carrollian limit vanishes. 16 Hence the various kinematical quantities such as the vorticity and the acceleration are purely geometric and originate from the temporal Carrollian frame used to describe the surface S . As we will see later, they turn out to be k → 0 counterparts of their relativistic homologues defined in (2.9), (2.10), (2.11) (see also (3.14) for the expansion and shear).…”

Section: The Carrollian Geometry: Connection and Curvaturementioning

confidence: 99%

“…We can define the curvature associated with a connection, by computing the commutator 16 A Carrollian fluid is always at rest, but could generally be obtained from a relativistic fluid moving at v i = k 2 β i + O k 4 . In this case, the "inverse velocity" β i would contribute to the kinematics and the dynamics of the fluid (see [52]).…”

Section: The Carrollian Geometry: Connection and Curvaturementioning

confidence: 99%

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Flat holography and Carrollian fluids

Ciambelli

Marteau

Petkou

et al. 2018

J. High Energ. Phys.

138

149

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We show that a holographic description of four-dimensional asymptotically locally flat spacetimes is reached smoothly from the zero-cosmological-constant limit of anti-de Sitter holography. To this end, we use the derivative expansion of fluid/gravity correspondence. From the boundary perspective, the vanishing of the bulk cosmological constant appears as the zero velocity of light limit. This sets how Carrollian geometry emerges in flat holography. The new boundary data are a two-dimensional spatial surface, identified with the null infinity of the bulk Ricci-flat spacetime, accompanied with a Carrollian time and equipped with a Carrollian structure, plus the dynamical observables of a conformal Carrollian fluid. These are the energy, the viscous stress tensors and the heat currents, whereas the Carrollian geometry is gathered by a two-dimensional spatial metric, a frame connection and a scale factor. The reconstruction of Ricci-flat spacetimes from Carrollian boundary data is conducted with a flat derivative expansion, resummed in a closed form in Eddington-Finkelstein gauge under further integrability conditions inherited from the ancestor anti-de Sitter set-up. These conditions are hinged on a duality relationship among fluid friction tensors and Cotton-like geometric data. We illustrate these results in the case of conformal Carrollian perfect fluids and Robinson-Trautman viscous hydrodynamics. The former are dual to the asymptotically flat Kerr-Taub-NUT family, while the latter leads to the homonymous class of algebraically special Ricci-flat spacetimes.

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Rigid limit for hypermultiplets and five-dimensional gauge theories

Cited by 18 publications

References 82 publications

Black Holes and Higher Depth Mock Modular Forms

Black Holes and Higher Depth Mock Modular Forms

Exploring 5d BPS Spectra with Exponential Networks

Flat holography and Carrollian fluids

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