Wall crossing from Boltzmann black hole halos
By J. Manschot, B. Pioline, Ashoke Sen. 2010
164 citations recorded by the source corpus.
A key question in the study of $ \mathcal{N} = 2 $ supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound states as multi-centered black hole solutions in $ \mathcal{N} = 2 $ supergravity, we provide two fully general and explicit formulæ for the change in the (refined) index across the wall. The first, “Higgs branch” formula relies on Reineke’s results for invariants of quivers without oriented loops, specialized to the Abelian case. The second, “Coulomb branch” formula results from evaluating the symplectic volume of the classical phase space of multi-centered solutions by localization. We provide extensive evidence that these new formulæ agree with each other and with the mathematical results of Kontsevich and Soibelman (KS) and Joyce and Song (JS). The main physical insight behind our results is that the Bose-Fermi statistics of individual black holes participating in the bound state can be traded for Maxwell-Boltzmann statistics, provided the (integer) index Ω(γ) of the internal degrees of freedom carried by each black hole is replaced by an effective (rational) index $ \bar{\Omega }\left( \gamma \right) = \sum\nolimits_{\left. m \right|\gamma } {{{{\Omega \left( {{{\gamma } \left/ {m} \right.}} \right)}} \left/ {{{m^2}}} \right.}} $ similar map also exists for the refined index. This observation provides a physical rationale for the appearance of the rational Donaldson-Thomas invariant $ \bar{\Omega }\left( \gamma \right) $ in the works of KS and JS.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9c5788fcad987d4c9047846d0617b028e06ad4ad
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In Nuclear and High Energy Physics
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Citations in the corpus
- Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012, background): “ity is closely correlated with the wall-crossing phenomenon. The wall-crossing phenomenon in N= 2 case corresponds to jumps in the Donaldson-Thomas invariants and is known to be much more complicated [48, 78, 76, 88]. It would be interesting though to dene the analog of the counting function for the”
- Witten index and wall crossing (2014, methodology): “[26, 28, 29] can be used not only for Coulomb branches of quiver theories but also for any multi-center bound state problems in R(3) with four supersymmetries, so I {Ai} makes sense as a multi-center index.”