Browsing by Author "Lee, Seung-Joo"

Now showing 1 - 6 of 6
  • Thumbnail Image
    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.
  • Thumbnail Image
    Fibrations in CICY threefolds
    Anderson, Lara B.; Gao, Xin; Gray, James A.; Lee, Seung-Joo (Springer, 2017-10-11)
    In this work we systematically enumerate genus one fibrations in the class of 7; 890 Calabi-Yau manifolds defined as complete intersections in products of projective spaces, the so-called CICY threefolds. This survey is independent of the description of the manifolds and improves upon past approaches that probed only a particular algebraic form of the threefolds (i.e. searches for "obvious" genus one fibrations as in [1, 2]). We also study K3-fibrations and nested fibration structures. That is, K3 fibrations with potentially many distinct elliptic fibrations. To accomplish this survey a number of new geometric tools are developed including a determination of the full topology of all CICY threefolds, including triple intersection numbers. In 2; 946 cases this involves finding a new "favorable" description of the manifold in which all divisors descend from a simple ambient space. Our results consist of a survey of obvious fibrations for all CICY threefolds and a complete classification of all genus one fibrations for 4; 957 "Kahler favorable" CICYs whose Kahler cones descend from a simple ambient space. Within the CICY dataset, we find 139; 597 obvious genus one fibrations, 30; 974 obvious K3 fibrations and 208; 987 nested combinations. For the Kahler favorable geometries we find a complete classification of 377; 559 genus one fibrations. For one manifold with Hodge numbers (19; 19) we find an explicit description of an in finite number of distinct genus-one fibrations extending previous results for this particular geometry that have appeared in the literature. The data associated to this scan is available here [3].
  • Thumbnail Image
    Multiple fibrations in Calabi-Yau geometry and string dualities
    Anderson, Lara B.; Gao, Xin; Gray, James A.; Lee, Seung-Joo (Springer, 2016-10-19)
    In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA, and heterotic string theories. Our results include many M-/F-theory correspondences in which distinct F-theory vacua - associated to different elliptic fibrations of the same CY n-fold - give rise to the same M-theory limit in one dimension lower. Examples include 5-dimensional correspondences between 6-dimensional theories with Abelian, non-Abelian and superconformal structure, as well as examples of higher rank Mordell-Weil geometries. In addition, in the context of heterotic/F-theory duality, we investigate the role played by multiple K3- and elliptic fibrations in known and novel string dualities in 8-, 6- and 4-dimensional theories. Here we systematically summarize nested fibration structures and comment on the roles they play in T-duality, mirror symmetry, and 4-dimensional compactifications of F-theory with G-flux. This investigation of duality structures is made possible by geometric tools developed in a companion paper [1].
  • Thumbnail Image
    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.
  • Thumbnail Image
    Tools for CICYs in F-theory
    Anderson, Lara B.; Gao, Xin; Gray, James A.; Lee, Seung-Joo (Springer, 2016-11-02)
    We provide a set of tools for analyzing the geometry of elliptically fibered Calabi-Yau manifolds, starting with a description of the total space rather than with a Weierstrass model or a specified type of fi ber/base. Such an approach to the subject of F-theory compactification makes certain geometric properties, which are usually hidden, manifest. Specifically, we review how to isolate genus-one fi brations in such geometries and then describe how to find their sections explicitly. This includes a full parameterization of the Mordell-Weil group where non-trivial. We then describe how to analyze the associated Weierstrass models, Jacobians and resolved geometries. We illustrate our discussion with concrete examples which are complete intersections in products of projective spaces (CICYs). The examples presented include cases exhibiting non-abelian symmetries and higher rank Mordell-Weil group. We also make some comments on non-flat fi brations in this context. In a companion paper [1] to this one, these results will be used to analyze the consequences for string dualities of the ubiquity of multiple fi brations in known constructions of Calabi-Yau manifolds.
  • Thumbnail Image
    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).