Browsing by Author "Yi, Piljin"

Now showing 1 - 3 of 3
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    D-particles on orientifolds and rational invariants
    Lee, Seung-Joo; Yi, Piljin (Springer, 2017-07-11)
    We revisit the DO bound state problems, of the M/IIA duality, with the Orientifolds. The cases of 04 and 08 have been studied recently, from the perspective of five-dimensional theories, while the case of O0 has been much neglected. The computation we perform for D0-O0 states boils down to the Witten indices for N = 16 O(m) and Sp(n) quantum mechanics, where we adapt and extend previous analysis by the authors. The twisted partition function Omega, obtained via localization, proves to be rational, and we establish a precise relation between Omega and the integral Witten index I, by identifying continuum contributions sector by sector. The resulting Witten index shows surprisingly large numbers of threshold bound states but in a manner consistent with M-theory. We close with an exploration on how the ubiquitous rational invariants of the wall-crossing physics would generalize to theories with Orientifolds.
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    Mutation, Witten index, and quiver invariant
    Kim, Heeyeon; Lee, Seung-Joo; Yi, Piljin (Springer, 2015-07-20)
    We explore Seiberg-like dualities, or mutations, for quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.
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    Witten index for noncompact dynamics
    Lee, Seung-Joo; Yi, Piljin (Springer, 2016-06-16)
    Among gauged dynamics motivated by string theory, we find many with gapless asymptotic directions. Although the natural boundary condition for ground states is L-2, one often turns on chemical potentials or supersymmetric mass terms to regulate the infrared issues, instead, and computes the twisted partition function. We point out how this procedure generically fails to capture physical L-2 Witten index with often misleading results. We also explore how, nevertheless, the Witten index is sometimes intricately embedded in such twisted partition functions. For d = 1 theories with gapless continuum sector from gauge multiplets, such as non-primitive quivers and pure Yang-Mills, a further subtlety exists, leading to fractional expressions. Quite unexpectedly, however, the integral L-2 Witten index can be extracted directly and easily from the twisted partition function of such theories. This phenomenon is tied to the notion of the rational invariant that appears naturally in the wall-crossing formulae, and offers a general mechanism of reading off Witten index directly from the twisted partition function. Along the way, we correct early numerical results for some of N = 4; 8; 16 pure Yang-Mills quantum mechanics, and count threshold bound states for general gauge groups beyond SU(N).