arXiv subjects

Daniel S. Park

Publications and source records attributed to Daniel S. Park.

31 records · Page 2Linked to original sources

arXiv2016

Tall sections from non-minimal transformations

In previous work, we have shown that elliptic fibrations with two sections, or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass model of a certain form, namely, the Jacobian of a $\mathbb{P}^{112}$ model. Most constructions of elliptically fibered Calabi-Yau manifolds with two sections have been carried out assuming that the image of this birational map was a "minimal" Weierstrass model. In this paper, we show that for some elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the Jacobian of the $\mathbb{P}^{112}$ model is not minimal. Said another way, starting from a Calabi-Yau Weierstrass model, the total space must be blown up (thereby destroying the "Calabi-Yau" property) in order to embed the model into $\mathbb{P}^{112}$. In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.

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arXiv2015

The equivariant A-twist and gauged linear sigma models on the two-sphere

We study two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on the $Ω$-deformed sphere, $S^2_Ω$, which is a one-parameter deformation of the $A$-twisted sphere. We provide an exact formula for the $S^2_Ω$ supersymmetric correlation functions using supersymmetric localization. The contribution of each instanton sector is given in terms of a Jeffrey-Kirwan residue on the Coulomb branch. In the limit of vanishing $Ω$-deformation, the localization formula greatly simplifies the computation of $A$-twisted correlation functions, and leads to new results for non-abelian theories. We discuss a number of examples and comment on the $ε_Ω$-deformation of the quantum cohomology relations. Finally, we present a complementary Higgs branch localization scheme in the special case of abelian gauge groups.

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arXiv2015

Topological charges in 2d N=(2,2) theories and massive BPS states

We study how charges of global symmetries that are manifest in the ultra-violet definition of a theory are realized as topological charges in its infra-red effective theory for two-dimensional theories with $\mathcal{N}=(2,2)$ supersymmetry. We focus on the charges that the states living on $S^1$ carry. The central charge---or BPS masses---of the supersymmetry algebra play a crucial role in making this correspondence precise. We study two examples: $U(1)$ gauge theories with chiral matter, and world-volume theories of "dynamical surface operators" of 4d $\mathcal{N}=2$ gauge theories. In the former example, we show that the flavor charges of the theory are realized as topological winding numbers in the effective theory on the Coulomb branch. In the latter, we show that there is a one-to-one correspondence between topological charges of the effective theory of the dynamical surface operator and the electric, magnetic, and flavor charges of the 4d gauge theory. We also examine the topologically charged massive BPS states on $S^1$ and discover that the massive BPS spectrum is sensitive to the radius of the circle in the simplest theory---the free theory of a periodic twisted chiral field. We clarify this behavior by showing that the massive BPS spectrum on $S^1$, unlike the BPS ground states, cannot be identified as elements of a cohomology.

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arXiv2015

On the Defect Group of a 6D SCFT

We use the F-theory realization of 6D superconformal field theories (SCFTs) to study the corresponding spectrum of stringlike, i.e. surface defects. On the tensor branch, all of the stringlike excitations pick up a finite tension, and there is a corresponding lattice of string charges, as well as a dual lattice of charges for the surface defects. The defect group is data intrinsic to the SCFT and measures the surface defect charges which are not screened by dynamical strings. When non-trivial, it indicates that the associated theory has a partition vector rather than a partition function. We compute the defect group for all known 6D SCFTs, and find that it is just the abelianization of the discrete subgroup of U(2) which appears in the classification of 6D SCFTs realized in F-theory. We also explain how the defect group specifies defining data in the compactification of a (1,0) SCFT.

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arXiv2014

6D SCFTs and Gravity

We study how to couple a 6D superconformal field theory (SCFT) to gravity. In F-theory, the models in question are obtained working on the supersymmetric background R^{5,1} x B where B is the base of a compact elliptically fibered Calabi-Yau threefold in which two-cycles have contracted to zero size. When the base has orbifold singularities, we find that the anomaly polynomial of the 6D SCFTs can be understood purely in terms of the intersection theory of fractional divisors: the anomaly coefficient vectors are identified with elements of the orbifold homology. This also explains why in certain cases, the SCFT can appear to contribute a "fraction of a hypermultiplet" to the anomaly polynomial. Quantization of the lattice of string charges also predicts the existence of additional light states beyond those captured by such fractional divisors. This amounts to a refinement to the lattice of divisors in the resolved geometry. We illustrate these general considerations with explicit examples, focusing on the case of F-theory on an elliptic Calabi-Yau threefold with base P^2 / Z_3.

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arXiv2014

Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories

We interpret certain Seiberg-like dualities of two-dimensional N=(2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the complexified Fayet-Iliopoulos parameters of the gauge group factors transform under those dualities and observe that they are in fact related to the dual cluster variables of cluster algebras. This implies that there is an underlying cluster algebra structure in the quantum Kahler moduli space of manifolds constructed from the corresponding Kahler quotients. We study the S^2 partition function of the gauge theories, showing that it is invariant under dualities/mutations, up to an overall normalization factor whose physical origin and consequences we spell out in detail. We also present similar dualities in N=(2,2)* quiver gauge theories, which are related to dualities of quantum integrable spin chains.

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arXiv2012

The Seiberg-Witten Kahler Potential as a Two-Sphere Partition Function

Recently it has been shown that the two-sphere partition function of a gauged linear sigma model of a Calabi-Yau manifold yields the exact quantum Kahler potential of the Kahler moduli space of that manifold. Since four-dimensional N=2 gauge theories can be engineered by non-compact Calabi-Yau threefolds, this implies that it is possible to obtain exact gauge theory Kahler potentials from two-sphere partition functions. In this paper, we demonstrate that the Seiberg-Witten Kahler potential can indeed be obtained as a two-sphere partition function. To be precise, we extract the quantum Kahler metric of 4D N=2 SU(2) Super-Yang-Mills theory by taking the field theory limit of the Kahler parameters of the O(-2,-2) bundle over P1 x P1. We expect this method of computing the Kahler potential to generalize to other four-dimensional N=2 gauge theories that can be geometrically engineered by toric Calabi-Yau threefolds.

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arXiv2012

F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds

The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X. After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study Calabi-Yau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations --- which relate the Neron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold --- serve as an important tool in our analysis.

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arXiv2012

Anomaly Equations and Intersection Theory

Six-dimensional supergravity theories with N=(1,0) supersymmetry must satisfy anomaly equations. These equations come from demanding the cancellation of gravitational, gauge and mixed anomalies. The anomaly equations have implications for the geometrical data of Calabi-Yau threefolds, since F-theory compactified on an elliptically fibered Calabi-Yau threefold with a section generates a consistent six-dimensional N=(1,0) supergravity theory. In this paper, we show that the anomaly equations can be summarized by three intersection theory identities. In the process we also identify the geometric counterpart of the anomaly coefficients---in particular, those of the abelian gauge groups---that govern the low-energy dynamics of the theory. We discuss the results in the context of investigating string universality in six dimensions.

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arXiv2012

Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry

We study six-dimensional N=(1,0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups - including abelian factors - and non-abelian matter representations is finite. We also identify infinite families of theories with distinct U(1) charges that cannot be ruled out using known quantum consistency conditions, though only a finite subset of these can arise from known string constructions.

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arXiv2012

Scalar Three-point Functions in a CDL Background

Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we compute the three-point function of a scalar field in a Coleman-De Luccia instanton background. We first compute the three-point function of the scalar field making only very mild assumptions about the scalar potential and the instanton background. We obtain the three-point function for points in the FRW patch of the CDL instanton and take two interesting limits; the limit where the three points are near the boundary of the hyperbolic slices of the FRW patch, and the limit where the three points lie on the past lightcone of the FRW patch. We expand the past lightcone three-point function in spherical harmonics. We show that the near boundary limit expansion of the three-point function of a massless scalar field exhibits conformal structure compatible with FRW-CFT when the FRW patch is flat. We also compute the three-point function when the scalar is massive, and explain the obstacles to generalizing the conjectured field-operator correspondence of massless fields to massive fields.

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arXiv2011

6D supergravity without tensor multiplets

We systematically investigate the finite set of possible gauge groups and matter content for N = 1 supergravity theories in six dimensions with no tensor multiplets, focusing on nonabelian gauge groups which are a product of SU(N) factors. We identify a number of models which obey all known low-energy consistency conditions, but which have no known string theory realization. Many of these models contain novel matter representations, suggesting possible new string theory constructions. Many of the most exotic matter structures arise in models which precisely saturate the gravitational anomaly bound on the number of hypermultiplets. Such models have a rigid symmetry structure, in the sense that there are no moduli which leave the full gauge group unbroken.

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arXiv2009

Graviton and Scalar Two-Point Functions in a CDL Background for General Dimensions

We compute the two-point functions of the scalar and graviton in a Coleman-De Luccia type instanton background in general dimensions. These are analytically continued to Lorentzian signature. We write the correlator in a form convenient for examining the "holographic" properties of this background inspired by the work of Freivogel, Sekino, Susskind and Yeh(FSSY). Based on this, we speculate on what kind of boundary theory we would have on this background if we assume that there exists a holographic duality.

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