, On the other hand, setting a field to zero, solves two F-term equations automatically. The remaining one defines a complete intersection manifold in the product of projective spaces. Requiring the dimension of this manifold to be non-negative gives the condition a + b ? c + 2 and permutations. When we set the FI parameters to zero, these projective spaces collapse to a point and so does the intersection manifold. As a result we do not have any condition on (a, b, c). This is rather puzzling as physically one would have expected to get some version of triangle inequality
Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett, vol.116, issue.6, p.61102, 2016. ,
First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J, vol.875, issue.1, p.1, 2019. ,
The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys, vol.2, pp.231-252, 1998. ,
Supersymmetric gauge theories and the AdS / CFT correspondence, Strings, Branes and Extra Dimensions: TASI 2001: Proceedings, pp.3-158, 2002. ,
Black Holes in String Theory, Springer Proc. Phys, vol.144, pp.59-178, 2013. ,
Extremal black holes and elementary string states, Mod. Phys. Lett, vol.10, pp.2081-2094, 1995. ,
Exact counting of black hole microstates, Phys. Rev. Lett, vol.94, p.241301, 2005. ,
Microscopic Origin of the Bekenstein-Hawking Entropy, Phys. Lett, vol.379, pp.99-104, 1996. ,
The fuzzball proposal for black holes: An elementary review, Fortsch. Phys, vol.53, pp.793-827, 2005. ,
The String dual of a confining four-dimensional gauge theory ,
Counting supertubes, JHEP, vol.06, p.28, 2004. ,
D1-D5 black hole microstate counting from supergravity, JHEP, issue.01, p.63, 2006. ,
Phase moduli space of supertubes, Nucl. Phys, vol.696, pp.251-262, 2004. ,
A geometric look on the microstates of supertubes, Nucl. Phys, vol.712, pp.115-138, 2005. ,
Black holes, black rings and their microstates, Lect. Notes Phys, vol.755, pp.1-92, 2008. ,
The fuzzball proposal for black holes, Phys. Rept, vol.467, pp.117-171, 2008. ,
A correspondence principle for black holes and strings, Phys. Rev, vol.55, pp.6189-6197, 1997. ,
Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP, issue.0008, p.52, 2000. ,
Bubbling AdS space and 1/2 BPS geometries, JHEP, issue.10, p.25, 2004. ,
The information paradox: A pedagogical introduction, Class. Quant. Grav, vol.26, p.224001, 2009. ,
Soft Hair on Black Holes, Phys. Rev. Lett, vol.116, issue.23, p.231301, 2016. ,
On the interior geometry of a typical black hole microstate ,
Four-center bubbled BPS solutions with a Gibbons-Hawking base, JHEP, issue.10, p.9, 2017. ,
URL : https://hal.archives-ouvertes.fr/cea-01513111
A systematic construction of microstate geometries with low angular momentum, JHEP, issue.10, p.217, 2017. ,
URL : https://hal.archives-ouvertes.fr/cea-01626969
AdS 2 holography: mind the cap, JHEP, vol.12, p.28, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01823329
The full space of BPS multicenter states with pure D-brane charges ,
URL : https://hal.archives-ouvertes.fr/hal-01914511
Bubbling the NHEK, JHEP, vol.01, p.108, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01945026
, Superstratum Symbiosis
URL : https://hal.archives-ouvertes.fr/hal-02088888
Thermal Decay without Information Loss in Horizonless Microstate Geometries ,
URL : https://hal.archives-ouvertes.fr/hal-02148880
Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP, issue.05, p.110, 2015. ,
URL : https://hal.archives-ouvertes.fr/cea-01180196
Supercharging Superstrata ,
On the General Theory of Relativity, Addendum: Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.), vol.1915, p.799, 1915. ,
, The Large Scale Structure of Space-Time. Cambridge Monographs on Mathematical Physics, 2011.
, General Relativity. Chicago Univ. Pr, 1984.
Gravitational collapse: The role of general relativity, Riv. Nuovo Cim, vol.1, p.1141, 1969. ,
Black holes and the second law, Lett. Nuovo Cim, vol.4, pp.737-740, 1972. ,
Extraction of rotational energy from a black hole, Nature, vol.229, pp.177-179, 1971. ,
Particle Creation by Black Holes, Commun. Math. Phys, vol.43, p.206, 1975. ,
All Possible Symmetries of the S Matrix, Phys. Rev, vol.159, pp.1251-1256, 1967. ,
Supergravity Theory in Eleven-Dimensions, Phys. Lett, vol.76, pp.409-412, 1978. ,
, TASI Lectures on Supergravity and String Vacua in Various Dimensions
String theory, vol.2, 1998. ,
Stability of Classical Solutions, Sov. J. Nucl. Phys, vol.24, p.449, 1976. ,
An Exact Classical Solution for the 't Hooft Monopole and the Julia-Zee Dyon, Phys. Rev. Lett, vol.35, pp.760-762, 1975. ,
The Geometry of D = 11 killing spinors, JHEP, vol.0304, p.39, 2003. ,
Basic concepts of string theory, Theoretical and Mathematical Physics, 2013. ,
Symmetries and Transformations of Chiral N=2 D=10 Supergravity, Phys. Lett, vol.126, pp.301-304, 1983. ,
Covariant Field Equations of Chiral N=2 D=10 Supergravity, Nucl. Phys, vol.226, 1983. ,
The Complete N=2, D=10 Supergravity, Nucl. Phys, vol.238, pp.181-220, 1984. ,
Massive N=2a Supergravity in Ten-Dimensions, Phys. Lett, vol.169, 1985. ,
String theory dynamics in various dimensions, Nucl. Phys, vol.443, pp.85-126, 1995. ,
Flux compactifications in string theory: A Comprehensive review, Phys. Rept, vol.423, pp.91-158, 2006. ,
A Symmetry of the String Background Field Equations, Phys. Lett, vol.194, pp.59-62, 1987. ,
U duality as general coordinate transformations, and space-time geometry, Int. J. Mod. Phys, vol.14, pp.4915-4942, 1999. ,
N=2 heterotic superstring and its dual theory in five-dimensions, Nucl. Phys, vol.460, pp.489-505, 1996. ,
The Geometry of N=2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys, vol.242, pp.244-268, 1984. ,
Gauging the d = 5 Maxwell-Einstein Supergravity Theories: More on Jordan Algebras, Nucl. Phys, vol.253, 1985. ,
Matter and Gauge Couplings of N=2 Supergravity in Six-Dimensions, Phys. Lett, vol.144, pp.187-192, 1984. ,
Tensor and vector multiplets in six-dimensional supergravity, Nucl. Phys, vol.519, pp.115-140, 1998. ,
All supersymmetric solutions of minimal supergravity in six dimensions, Class. Quant. Grav, vol.20, pp.5049-5078, 2003. ,
The General form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six-dimensions, Class. Quant. Grav, vol.21, pp.3171-3196, 2004. ,
A New Anomaly Free Chiral Supergravity Theory From Compactification on K3, Phys. Lett, vol.139, pp.283-287, 1984. ,
Low-energy analysis of M and F theories on Calabi-Yau threefolds, Nucl. Phys, vol.474, pp.323-342, 1996. ,
An Orientifold of type IIB theory on K3, Nucl. Phys, vol.472, pp.207-220, 1996. ,
K3 orientifolds, Nucl. Phys, vol.477, pp.715-745, 1996. ,
Multiple realizations of N=1 vacua in six-dimensions, Nucl. Phys, vol.479, pp.285-304, 1996. ,
D = 6, N=1 string vacua and duality, Dualities in gauge and string theories. Proceedings, APCTP, pp.230-282, 1997. ,
Structure of Six-Dimensional Microstate Geometries, JHEP, issue.09, p.75, 2015. ,
General supersymmetric AdS(5) black holes, JHEP, issue.04, p.48, 2004. ,
BPS black holes in N=2 five-dimensional AdS supergravity, Phys. Lett, vol.442, pp.97-101, 1998. ,
Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev, vol.62, p.24003, 2000. ,
Global structure of five-dimensional fuzzballs, Class.Quant.Grav, vol.31, p.25016, 2014. ,
Evanescent ergosurfaces and ambipolar hyperkler metrics, JHEP, issue.04, p.130, 2016. ,
Kaluza-klein monopole, Phys. Rev. Lett, vol.51, pp.87-90, 1983. ,
Magnetic monopoles in kaluza-klein theories, Nuclear Physics B, vol.226, issue.1, pp.29-48, 1983. ,
Supergravity flows and D-brane stability, JHEP, issue.0008, p.50, 2000. ,
The foaming three-charge black hole, Phys. Rev, vol.75, p.124026, 2007. ,
Supergravity microstates for BPS black holes and black rings, JHEP, issue.0606, p.7, 2006. ,
Bubbling supertubes and foaming black holes, Phys. Rev, vol.74, p.66001, 2006. ,
Bound states of spinning black holes in five dimensions, JHEP, issue.05, p.101, 2017. ,
Spectral Flow, and the Spectrum of Multi-Center Solutions, Phys. Rev, vol.77, p.125025, 2008. ,
U-duality and non-BPS solutions, JHEP, issue.02, p.74, 2011. ,
, Supertubes in Bubbling Backgrounds: Born-Infeld Meets Supergravity, p.106, 2009.
D-branes and spinning black holes, Phys.Lett, vol.391, pp.93-98, 1997. ,
Mergers and Typical Black Hole Microstates, JHEP, issue.11, p.42, 2006. ,
Plumbing the Abyss: Black Ring Microstates, JHEP, issue.07, p.19, 2008. ,
Quantum quivers and Hall / hole halos, JHEP, issue.0210, p.23, 2002. ,
Supertubes, Phys. Rev. Lett, vol.87, p.11602, 2001. ,
Supercurves, Phys. Lett, vol.538, pp.366-374, 2002. ,
Supergravity supertubes, JHEP, issue.07, p.11, 2001. ,
Tachyons, supertubes and brane / anti-brane systems, JHEP, issue.03, p.16, 2002. ,
AdS/CFT duality and the black hole information paradox, Nucl. Phys, vol.623, pp.342-394, 2002. ,
All the supersymmetric solutions of ungauged N = (1, 0), d = 6 supergravity ,
BPS solutions of six-dimensional (1, 0) supergravity coupled to tensor multiplets, JHEP, issue.06, p.21, 2018. ,
Supersymmetric Solutions in Six Dimensions: A Linear Structure, JHEP, issue.1203, p.84, 2012. ,
URL : https://hal.archives-ouvertes.fr/cea-00825799
6D microstate geometries from 10D structures, Nucl.Phys, vol.876, pp.509-555, 2013. ,
Superdescendants of the D1D5 CFT and their dual 3-charge geometries, JHEP, vol.1403, p.7, 2014. ,
Momentum Fractionation on Superstrata, JHEP, issue.05, p.64, 2016. ,
URL : https://hal.archives-ouvertes.fr/cea-01508022
Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett, vol.117, issue.20, p.201601, 2016. ,
URL : https://hal.archives-ouvertes.fr/cea-01507729
M-theory Superstrata and the MSW String, JHEP, issue.06, p.137, 2017. ,
URL : https://hal.archives-ouvertes.fr/cea-01505699
Asymptotically-flat supergravity solutions deep inside the black-hole regime, JHEP, issue.02, p.14, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01704828
Adding new hair to the 3-charge black ring, Class.Quant.Grav, vol.29, p.85006, 2012. ,
Constructing 'hair' for the three charge hole, Nucl. Phys, vol.680, pp.415-449, 2004. ,
The Black hole in three-dimensional space-time, Phys. Rev. Lett, vol.69, pp.1849-1851, 1992. ,
Metric of the multiply wound rotating string, Nucl. Phys, vol.610, pp.49-76, 2001. ,
Gravity solutions for the D1-D5 system with angular momentum ,
Fuzzballs with internal excitations, JHEP, issue.06, p.56, 2007. ,
Oscillating supertubes and neutral rotating black hole microstates, JHEP, vol.1404, p.72, 2014. ,
Coiffured Black Rings, Class.Quant.Grav, vol.31, p.165015, 2014. ,
URL : https://hal.archives-ouvertes.fr/cea-01120750
, The D1/D5 system and singular CFT, p.17, 1999.
U(1) charges and moduli in the D1-D5 system, JHEP, issue.06, p.19, 1999. ,
Microstates at the boundary of AdS, JHEP, issue.05, p.14, 2012. ,
Microscopic formulation of black holes in string theory, Phys. Rept, vol.369, pp.549-686, 2002. ,
Holographic anatomy of fuzzballs, JHEP, issue.04, p.23, 2007. ,
A non-renormalization theorem for chiral primary 3-point functions, JHEP, issue.07, p.137, 2012. ,
Integrability and Black-Hole Microstate Geometries, JHEP, issue.11, p.21, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01645730
Tidal Stresses and Energy Gaps in Microstate Geometries, JHEP, vol.02, p.122, 2018. ,
Early Scrambling and Capped BTZ Geometries ,
URL : https://hal.archives-ouvertes.fr/hal-01974797
Nonextreme black holes from nonextreme intersecting M-branes, Nucl. Phys, vol.478, pp.181-198, 1996. ,
Macroscopic and microscopic entropy of near extremal spinning black holes, Phys.Lett, vol.381, pp.423-426, 1996. ,
General Rotating Five Dimensional Black Holes of Toroidally Compactified Heterotic String, Nucl. Phys, vol.476, pp.118-132, 1996. ,
Near horizon geometry of rotating black holes in five dimensions, Nucl. Phys, vol.531, pp.239-255, 1998. ,
Microscopic theory of black hole superradiance, Phys. Rev, vol.77, p.64018, 2008. ,
Microscopic Realization of the Kerr/CFT Correspondence, JHEP, vol.02, p.10, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00528851
D-brane Construction of the 5D NHEK Dual, JHEP, issue.07, p.176, 2012. ,
Kerr/CFT, dipole theories and nonrelativistic CFTs, JHEP, vol.12, p.9, 2012. ,
URL : https://hal.archives-ouvertes.fr/cea-00823321
Un-twisting the NHEK with spectral flows, JHEP, vol.1303, p.28, 2013. ,
URL : https://hal.archives-ouvertes.fr/cea-00843302
Black Hole Superradiance From Kerr/CFT, JHEP, issue.04, p.19, 2010. ,
Warped AdS(3) Black Holes, JHEP, issue.03, p.130, 2009. ,
Warped anti-de Sitter spaces from brane intersections in type II string theory, JHEP, issue.06, p.49, 2010. ,
Warped AdS3/Dipole-CFT Duality, JHEP, issue.05, p.120, 2012. ,
Almost BPS black holes, p.58, 2009. ,
Multi-Center non-BPS Black Holes -the Solution, p.32, 2009. ,
Non-BPS Black Rings and Black Holes in Taub-NUT, JHEP, issue.06, p.15, 2009. ,
Mind the Gap: Supersymmetry Breaking in Scaling, Microstate Geometries, JHEP, vol.1110, p.6, 2011. ,
A bubbling bolt, JHEP, vol.1407, p.118, 2014. ,
Non-BPS multi-bubble microstate geometries, JHEP, issue.02, p.73, 2016. ,
URL : https://hal.archives-ouvertes.fr/cea-01508030
Bolting Multicenter Solutions, JHEP, issue.01, p.127, 2017. ,
URL : https://hal.archives-ouvertes.fr/cea-01505707
An Infinite-Dimensional Family of Black-Hole Microstate Geometries, JHEP, vol.1103, p.22, 2011. ,
URL : https://hal.archives-ouvertes.fr/cea-00825829
One Thousand and One Bubbles, JHEP, vol.01, p.41, 2018. ,
Split states, entropy enigmas, holes and halos, JHEP, issue.11, p.129, 2011. ,
Wall Crossing from Boltzmann Black Hole Halos, JHEP, issue.07, p.59, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00533632
BPS State Counting in N=8 Supersymmetric String Theory for Pure D-brane Configurations, JHEP, issue.10, p.186, 2014. ,
Do All BPS Black Hole Microstates Carry Zero Angular Momentum?, JHEP, issue.04, p.82, 2016. ,
Counting dyons in N=8 string theory, JHEP, issue.06, p.37, 2006. ,
Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys, vol.185, pp.197-209, 1997. ,
, Counting BPS black holes in toroidal Type II string theory
Dyon spectrum in generic N=4 supersymmetric Z(N) orbifolds, JHEP, vol.01, p.16, 2007. ,
Split attractor flows and the spectrum of BPS D-branes on the quintic, JHEP, issue.05, p.12, 2001. ,
, Dis)assembling special Lagrangians
Exact solutions for supersymmetric stationary black hole composites, JHEP, vol.1111, p.127, 2011. ,
Four Dimensional Black Hole Microstates: From D-branes to Spacetime Foam, JHEP, issue.0801, p.56, 2008. ,
, Resolving the Structure of Black Holes: Philosophizing with a Hammer
URL : https://hal.archives-ouvertes.fr/cea-00973465
More on microstate geometries of 4d black holes, JHEP, issue.05, p.147, 2017. ,
Arithmetic of Quantum Entropy Function, p.68, 2009. ,
Supersymmetric Index from Black Hole Entropy, JHEP, issue.04, p.34, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00526770
D-branes, quivers, and ALE instantons ,
Scaling BPS Solutions and pure-Higgs States, JHEP, issue.1211, p.171, 2012. ,
URL : https://hal.archives-ouvertes.fr/cea-00822655
Quantum Black Holes, Wall Crossing, and Mock Modular Forms ,
All supersymmetric solutions of minimal supergravity in five-dimensions, Class.Quant.Grav, vol.20, pp.4587-4634, 2003. ,
On the Oscillation of Species, JHEP, vol.1409, p.113, 2014. ,
URL : https://hal.archives-ouvertes.fr/cea-00973442
The Kerr/CFT Correspondence, Phys.Rev, vol.80, p.124008, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00528860
Warped Conformal Field Theory, Phys. Rev, vol.86, p.124018, 2012. ,
AdS 3 : the NHEK generation, JHEP, issue.05, p.120, 2016. ,
D1-D5-P microstates at the cap, JHEP, vol.1302, p.50, 2013. ,
Holographic description of non-supersymmetric orbifolded D1-D5-P solutions, JHEP, issue.11, p.63, 2015. ,
Two Kissing Bolts ,
URL : https://hal.archives-ouvertes.fr/hal-01862071
The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105, Astrophys.J, vol.652, pp.518-539, 2006. ,
Black hole entropy in M-theory, JHEP, vol.12, p.2, 1997. ,
Exact microstate counting for dyonic black holes in AdS4, Phys. Lett, vol.771, pp.462-466, 2017. ,
A universal counting of black hole microstates in AdS 4, JHEP, issue.02, p.54, 2018. ,
AdS(2) quantum gravity and string theory, JHEP, vol.01, p.7, 1999. ,
Ads(3)/CFT(2) to Ads(2)/CFT(1), JHEP, issue.04, p.34, 2009. ,
What is a chiral 2d CFT? And what does it have to do with extremal black holes?, JHEP, issue.02, p.17, 2010. ,
States of a chiral 2d CFT, Class. Quant. Grav, vol.28, p.45004, 2011. ,
, Comments on AdS 2 Gravity
AdS 2 holographic dictionary, JHEP, vol.12, p.8, 2016. ,
Anti-de Sitter fragmentation, JHEP, vol.02, p.11, 1999. ,
Models of AdS 2 backreaction and holography, JHEP, issue.11, p.14, 2015. ,
A simple model of quantum holography, Talks at KITP, 2015. ,
Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev, vol.94, issue.10, p.106002, 2016. ,
Black Holes and Random Matrices, JHEP, issue.05, p.118, 2017. ,
Echoes of chaos from string theory black holes, JHEP, issue.03, p.154, 2017. ,
The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual ,
Bubbles on Manifolds with a U(1) Isometry, JHEP, issue.08, p.4, 2007. ,
Bubbling geometries for AdS 2 ×S 2, JHEP, vol.10, p.167, 2015. ,
State Operator Correspondence and Entanglement in AdS 2 /CF T 1, Entropy, vol.13, pp.1305-1323, 2011. ,
Holographic Description of AdS(2) Black Holes, JHEP, issue.11, p.52, 2008. ,
Conformal quantum mechanics as the CFT 1 dual to AdS 2, Phys. Lett, vol.701, pp.503-507, 2011. ,
Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics, Phys. Rev, vol.86, p.45017, 2012. ,
The Extreme Kerr throat geometry: A Vacuum analog of AdS(2) x S**2, Phys.Rev, vol.60, p.104030, 1999. ,
Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav, vol.40, pp.2249-2431, 2008. ,
Classification of near-horizon geometries of extremal black holes, Living Rev. Rel, vol.16, issue.8, 2013. ,
Unitary 4-point correlators from classical geometries, Eur. Phys. J. C78, vol.8, issue.1, 2018. ,
A Critique of the Fuzzball Program ,
Lecture notes on holographic renormalization, Class. Quant. Grav, vol.19, pp.5849-5876, 2002. ,
Minkowski space correlators in AdS / CFT correspondence: Recipe and applications, JHEP, issue.09, p.42, 2002. ,
Real-time gauge/gravity duality, Phys. Rev. Lett, vol.101, p.81601, 2008. ,
Real-time gauge/gravity duality: Prescription, Renormalization and Examples, JHEP, issue.05, p.85, 2009. ,
Real-time gauge/gravity duality and ingoing boundary conditions, Nucl. Phys. Proc, pp.193-196, 2009. ,
Correlators at large c without information loss, JHEP, issue.09, p.65, 2016. ,
Holographic 4-point correlators with heavy states, JHEP, issue.10, p.40, 2017. ,
AdS 3 four-point functions from 1 8 -BPS states ,
URL : https://hal.archives-ouvertes.fr/hal-02116554
, Holographic Correlators on Integrable Superstrata