Quantum quivers and Hall / hole halos

By Frederik Denef. 2002

402 citations recorded by the source corpus.

Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect, and to count ground state degeneracies of certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a non-renormalization theorem in N = 4 quantum mechanics for the first order part of the Lagrangian in an expansion in powers of velocity.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c236bdeaf5e0e78ff83e8a209896aecba49cce90

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Ashoke Sen
2. G. Moore
3. K. Hori
4. C. Vafa
5. P. Aspinwall
6. Clay Córdova
7. Frederik Denef
8. Michael R Douglas

In Nuclear and High Energy Physics

1. Ashoke Sen
2. Frederik Denef
3. G. Moore
4. B. Pioline
5. N. Warner
6. C. Vafa
7. I. Bena
8. Yuji Tachikawa

In Statistical and Nonlinear Physics

1. Ashoke Sen
2. B. Pioline
3. G. Moore
4. N. Warner
5. K. Hori
6. C. Vafa
7. Frederik Denef
8. Yuji Tachikawa

Citations in the corpus

• Localization in quiver moduli spaces (2009, background): “It has its origin in the relationship between the Euler characteristic of moduli spaces of quiver representations and the Witten index in superstring theory and the entropy of black holes respectively; see for instance [6].”
• Witten index and wall crossing (2014, methodology): “Everything is essentially obtained in [22].”
• Split states, entropy enigmas, holes and halos (2007, background): “The following gives a sketch of how this is done, based on the detailed study of analogous systems in [65], to which we refer for more details.”
• Classification of Complete N = 2 Supersymmetric Theories in 4 Dimensions (2011, background): “For example it is known that the BPS quiver for the pure SU(2) gauge theory is given by the affine Dynkin diagram Â1 [7].”
• Magnetic monopole dynamics, supersymmetry, and duality (2006, methodology): “(11)This field theory counting was precisely reproduced later by a string theory construction using D-branes wrapping special Lagrange submanifolds in a Calabi-Yau manifold [246].”
• Framed BPS states (2010, neutral): “The unusual-looking Z2 gradings have a beautiful physical explanation [28], ultimately related to the fact that the magnetic field forces the spin of the halo particle to point inwards.”
• Global structure of five-dimensional fuzzballs (2013, background): “Indeed, it was in this context that scaling solutions were first discovered and investigated [27, 34, 35] but it was not until later that the significance of scaling solutions for five-dimensional microstate geometries was discovered [30–32].”
• $\mathcal{N} = 2$ quantum field theories and their BPS quivers (2011, background): “1 Pure SU(2) The quiver for pure SU(2) gauge theory has been worked out in various papers [11, 13, 18, 28, 29].”
• Four dimensional black hole microstates: from D-branes to spacetime foam (2006, methodology): “As gs decreases further, the states can be described in the low-energy quiver gauge theory of a system of intersecting D-branes, following Denef [13].”
• N=2 Supersymmetric Dynamics for Pedestrians (2013, background): “This point of view was originally introduced in the context ofN=2 supergravity in [97].”
• Dirichlet Branes and Mirror Symmetry (2009, background): “Presumably this corresponds to some known cohomology theory [225, 110], but to our knowledge this has not been well understood.”
• Quantizing N = 2 multicenter solutions (2008, methodology): “3 Including the Fermionic Degrees of Freedom From the open string point of view [14] we know that (4.”
• Dying dyons don't count (2007, background): “The conserved angular momentum, after carefully quantizing the system [18], turns out to be 2J + 1 = |P ·Q| .”
• Black holes, black rings and their microstates (2007, methodology): “It is now evident that the four-dimensional two-center solution corresponding to black rings and supertubes in Taub-NUT [27, 58, 59, 60] is part of the family of multicenter solutions that have been explored by Denef and collaborators [71].”
• Black holes as effective geometries (2008, methodology): “As discussed in [44], the four-dimensional multicentred solutions can also be analysed in the probe approximation by studying the quiver quantum mechanics of D-branes in a multicentred supergravity background.”
• Black hole bound states in AdS(3) x S**2 (2008, methodology): “(6)Multicentered “scaling” or “abyss” solutions [19, 32, 33, 34], for which the centers’ coordinates can approach each other arbitrarily closely, are viewed as being continuously connected to single centered solutions, hence the split flow conjecture unfortunately does not say anything about the exi”