arXiv subjects

Sakura Schafer-Nameki

Publications and source records attributed to Sakura Schafer-Nameki.

At least 91 records · Page 5Linked to original sources

arXiv2019

5d Superconformal Field Theories and Graphs

We propose a graph-theoretic description to determine and characterize 5d superconformal field theories (SCFTs) that arise as circle reductions of 6d $\mathcal{N} = (1,0)$ SCFTs. Each 5d SCFT is captured by a graph, called a Combined Fiber Diagram (CFD). Transitions between CFDs encode mass deformations that trigger flows between SCFTs. In this way, the complete set of descendants of a given 6d theory are obtained from a single marginal CFD. The graphs encode key physical information like the superconformal flavor symmetry and BPS states. As an illustration, we ascertain the aforementioned data associated to all the 5d SCFTs descending from 6d minimal $(E_6, E_6)$ and $(D_k, D_k)$ conformal matter for any $k$. This includes predictions for thus far unknown flavor symmetry enhancements.

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arXiv2019

Higgs Bundles for M-theory on $G_2$-Manifolds

M-theory compactified on $G_2$-holonomy manifolds results in 4d $\mathcal{N}=1$ supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle $M_3$. We derive the BPS equations and find the massless spectrum for both abelian and non-abelian gauge groups in 4d. The mathematical tool that allows us to determine the spectrum is Morse theory, and more generally Morse-Bott theory. The latter generalization allows us to make contact with twisted connected sum (TCS) $G_2$-manifolds, which form the largest class of examples of compact $G_2$-manifolds. M-theory on TCS $G_2$-manifolds is known to result in a non-chiral 4d spectrum. We determine the Higgs bundle for this class of $G_2$-manifolds and provide a prescription for how to engineer singular transitions to models that have chiral matter in 4d.

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arXiv2018

F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections

We study elliptic fibrations for F-theory compactifications realizing 4d and 6d supersymmetric gauge theories with abelian gauge factors. In the fibration these U(1) symmetries are realized in terms of additional rational sections. We obtain a universal characterization of all the possible U(1) charges of matter fields by determining the corresponding codimension two fibers with rational sections. In view of modelling supersymmetric Grand Unified Theories, one of the main examples that we analyze are U(1) symmetries for SU(5) gauge theories with \bar{5} and 10 matter. We use a combination of constraints on the normal bundle of rational curves in Calabi-Yau three- and four-folds, as well as the splitting of rational curves in the fibers in codimension two, to determine the possible configurations of smooth rational sections. This analysis straightforwardly generalizes to multiple U(1)s. We study the flops of such fibers, as well as some of the Yukawa couplings in codimension three. Furthermore, we carry out a universal study of the U(1)-charged GUT singlets, including their KK-charges, and determine all realizations of singlet fibers. By giving vacuum expectation values to these singlets, we propose a systematic way to analyze the Higgsing of U(1)s to discrete gauge symmetries in F-theory.

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arXiv2018

An $\mathcal{N}=1$ 3d-3d Correspondence

M5-branes on an associative three-cycle $M_3$ in a $G_2$-holonomy manifold give rise to a 3d $\mathcal{N}=1$ supersymmetric gauge theory, $T_{\mathcal{N}=1} [M_3]$. We propose an $\mathcal{N}=1$ 3d-3d correspondence, based on two observables of these theories: the Witten index and the $S^3$-partition function. The Witten index of a 3d $\mathcal{N}=1$ theory $T_{\mathcal{N}=1} [M_3]$ is shown to be computed in terms of the partition function of a topological field theory, a super-BF-model coupled to a spinorial hypermultiplet (BFH), on $M_3$. The BFH-model localizes on solutions to a generalized set of 3d Seiberg-Witten equations on $M_3$. Evidence to support this correspondence is provided in the abelian case, as well as in terms of a direct derivation of the topological field theory by twisted dimensional reduction of the 6d $(2,0)$ theory. We also consider a correspondence for the $S^3$-partition function of the $T_{\mathcal{N}=1} [M_3]$ theories, by determining the dimensional reduction of the M5-brane theory on $S^3$. The resulting topological theory is Chern-Simons-Dirac theory, for a gauge field and a twisted harmonic spinor on $M_3$, whose equations of motion are the generalized 3d Seiberg-Witten equations. For generic $G_2$-manifolds the theory reduces to real Chern-Simons theory, in which case we conjecture that the $S^3$-partition function of $T_{\mathcal{N}=1}[M_3]$ is given by the Witten-Reshetikhin-Turaev invariant of $M_3$.

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arXiv2018

Theories of Class F and Anomalies

We consider the 6d (2,0) theory on a fibration by genus g curves, and dimensionally reduce along the fiber to 4d theories with duality defects. This generalizes class S theories, for which the fibration is trivial. The non-trivial fibration in the present setup implies that the gauge couplings of the 4d theory, which are encoded in the complex structures of the curve, vary and can undergo S-duality transformations. These monodromies occur around 2d loci in space-time, the duality defects, above which the fiber is singular. The key role that the fibration plays here motivates refering to this setup as theories of class F. In the simplest instance this gives rise to 4d N=4 Super-Yang-Mills with space-time dependent coupling that undergoes SL(2, Z) monodromies. We determine the anomaly polynomial for these theories by pushing forward the anomaly polynomial of the 6d (2,0) theory along the fiber. This gives rise to corrections to the anomaly polynomials of 4d N=4 SYM and theories of class S. For the torus case, this analysis is complemented with a field theoretic derivation of a U(1) anomaly in 4d N=4 SYM. The corresponding anomaly polynomial is tested against known expressions of anomalies for wrapped D3-branes with varying coupling, which are known field theoretically and from holography. Extensions of the construction to 4d N = 0 and 1, and 2d theories with varying coupling, are also discussed.

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arXiv2018

Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories

M-theory on compact eight-manifolds with $\mathrm{Spin}(7)$-holonomy is a framework for geometric engineering of 3d $\mathcal{N}=1$ gauge theories coupled to gravity. We propose a new construction of such $\mathrm{Spin}(7)$-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four-fold and a $G_2$-holonomy manifold times a circle, respectively, which both asymptote to a Calabi-Yau three-fold times a cylinder. The generalized connected sum construction is first exemplified for Joyce orbifolds, and is then used to construct examples of new compact manifolds with $\mathrm{Spin}(7)$-holonomy. In instances when there is a K3-fibration of the $\mathrm{Spin}(7)$-manifold, we test the spectra using duality to heterotic on a $T^3$-fibered $G_2$-holonomy manifold, which are shown to be precisely the recently discovered twisted-connected sum constructions.

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arXiv2018

Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds

We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S^3$. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of arXiv:1708.07215, which relates M-theory on TCS $G_2$-manifolds to $E_8\times E_8$ heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the $G_2$-compactification.

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arXiv2018

F-theory and AdS_3/CFT_2 (2,0)

We continue to develop the program initiated in arXiv:1705.04679 of studying supersymmetric AdS_3 solutions of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of 4d theories with varying coupling. Imposing 2d N=(0,2) supersymmetry, we derive the general conditions on the geometry for Type IIB AdS_3 solutions with varying axio-dilaton and five-form flux. We discuss a class of solutions, which extend AdS_3 x T^2 x M_5 Type IIB backgrounds, to F-theory geometries of the type AdS_3 x K3 x M_5 with varying axio-dilaton characterizing the elliptic fiber of the K3, and describe their dual field theories. For a specific choice of M_5 this corresponds to a family of solutions that are conjectured to be dual to twisted compactifications of 4d N=1 Y^{p,q} quiver gauge theories on a curve with varying coupling. For this setup, we compare the central charges from holography and field theory and find agreement to subleading order in N. Requiring enhanced 2d N=(2,2) supersymmetry we find that the axio-dilaton must be constant. However, if the internal geometry is allowed to be non-compact, we obtain the most general class of Type IIB AdS_5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs.

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arXiv2017

Chiral 2d Theories from N=4 SYM with Varying Coupling

We study 2d chiral theories arising from 4d N=4 Super-Yang Mills (SYM) with varying coupling tau. The 2d theory is obtained by dimensional reduction of N=4 SYM on a complex curve with a partial topological twist that accounts for the non-constant tau. The resulting 2d theories can preserve (0,n) with n = 2, 4, 6, 8 chiral supersymmetry, and have a natural realization in terms of strings from wrapped D3-branes in F-theory. We determine the twisted dimensional reduction, as well as the spectrum and anomaly polynomials of the resulting strings in various dimensions. We complement this by considering the dual M-theory configurations, which can either be realized in terms of M5-branes wrapped on complex surfaces, or M2-branes on curves that result in 1d supersymmetric quantum mechanics.

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arXiv2017

Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality

We study the duality between M-theory on compact holonomy G2-manifolds and the heterotic string on Calabi-Yau three-folds. The duality is studied for K3-fibered G2-manifolds, called twisted connected sums, which lend themselves to an application of fiber-wise M-theory/Heterotic Duality. For a large class of such G2-manifolds we are able to identify the dual heterotic as well as F-theory realizations. First we establish this chain of dualities for smooth G2-manifolds. This has a natural generalization to situations with non-abelian gauge groups, which correspond to singular G2-manifolds, where each of the K3-fibers degenerates. We argue for their existence through the chain of dualities, supported by non-trivial checks of the spectra. The corresponding 4d gauge groups can be both Higgsable and non-Higgsable, and we provide several explicit examples of the general construction.

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arXiv2017

F-theory and AdS_3/CFT_2

We construct supersymmetric AdS_3 solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d N=(0,4) superconformal field theories with small superconformal algebra. In F-theory these arise from D3-branes wrapped on curves in the base of an elliptically fibered Calabi-Yau threefold Y_3 and correspond to strings in the 6d N=(1,0) theory obtained from F-theory on Y_3. The non-trivial fibration over the wrapped curves implies a varying coupling of the N=4 Super-Yang-Mills theory on the D3-branes. We compute the holographic central charges and show that these agree with the field theory and with the anomalies of self-dual strings in 6d. We complement our analysis with a discussion of the dual M-theory solutions and a comparison of the central charges.

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arXiv2017

The Gravitational Sector of 2d (0,2) F-theory Vacua

F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S^1 reduction of the dual F-theory.

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arXiv2017

F-theory and 2d (0,2) Theories

F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.

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arXiv2016

Six-dimensional Origin of $\mathcal{N}=4$ SYM with Duality Defects

We study the topologically twisted compactification of the 6d $(2,0)$ M5-brane theory on an elliptically fibered Kähler three-fold preserving two supercharges. We show that upon reducing on the elliptic fiber, the 4d theory is $\mathcal{N}=4$ Super-Yang Mills, with varying complexified coupling $τ$, in the presence of defects. For abelian gauge group this agrees with the so-called duality twisted theory, and we determine a non-abelian generalization to $U(N)$. When the elliptic fibration is singular, the 4d theory contains 3d walls (along the branch-cuts of $τ$) and 2d surface defects, around which the 4d theory undergoes $SL(2,\mathbb{Z})$ duality transformations. Such duality defects carry chiral fields, which from the 6d point of view arise as modes of the two-form $B$ in the tensor multiplet. Each duality defect has a flavor symmetry associated to it, which is encoded in the structure of the singular elliptic fiber above the defect. Generically 2d surface defects will intersect in points in 4d, where there is an enhanced flavor symmetry. The 6d point of view provides a complete characterization of this 4d-3d-2d-0d `Matroshka'-defect configuration.

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arXiv2016

M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models

We study the 6d N=(0,2) superconformal field theory, which describes multiple M5-branes, on the product space S^2 x M_4, and suggest a correspondence between a 2d N=(0,2) half-twisted gauge theory on S^2 and a topological sigma-model on the four-manifold M_4. To set up this correspondence, we determine in this paper the dimensional reduction of the 6d N=(0,2) theory on a two-sphere and derive that the four-dimensional theory is a sigma-model into the moduli space of solutions to Nahm's equations, or equivalently the moduli space of k-centered SU(2) monopoles, where k is the number of M5-branes. We proceed in three steps: we reduce the 6d abelian theory to a 5d Super-Yang-Mills theory on I x M_4, with I an interval, then non-abelianize the 5d theory and finally reduce this to 4d. In the special case, when M_4 is a Hyper-Kahler manifold, we show that the dimensional reduction gives rise to a topological sigma-model based on tri-holomorphic maps. Deriving the theory on a general M_4 requires knowledge of the metric of the target space. For k=2 the target space is the Atiyah-Hitchin manifold and we twist the theory to obtain a topological sigma-model, which has both scalar fields and self-dual two-forms.

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arXiv2015

Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces

Box graphs, or equivalently Coulomb phases of three-dimensional N=2 supersymmetric gauge theories with matter, give a succinct, comprehensive and elegant characterization of crepant resolutions of singular elliptically fibered varieties. Furthermore, the box graphs predict that the phases are organized in terms of a network of flop transitions. The geometric construction of the resolutions associated to the phases is, however, a difficult problem. Here, we identify a correspondence between box graphs for the gauge algebras su(2k+1) with resolutions obtained using toric tops and generalizations thereof. Moreover, flop transitions between different such resolutions agree with those predicted by the box graphs. Our results thereby provide explicit realizations of the box graph resolutions.

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arXiv2015

Froggatt-Nielsen meets Mordell-Weil: A Phenomenological Survey of Global F-theory GUTs with U(1)s

In F-theory, U(1) gauge symmetries are encoded in rational sections, which generate the Mordell-Weil group of the elliptic fibration of the compactification space. Recently the possible U(1) charges for global SU(5) F-theory GUTs with smooth rational sections were classified arXiv:1504.05593 [hep-th]. In this paper we utilize this classification to probe global F-theory models for their phenomenological viability. After imposing an exotic-free MSSM spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the presence of U(1) gauge symmetries), absence of dimension four and five proton decay operators and other R-parity violating couplings, and the presence of at least the third generation top Yukawa coupling, we generate the remaining quark and lepton Yukawa textures by a Froggatt-Nielsen mechanism. In this process we require that the dangerous couplings are forbidden at leading order, and when re-generated by singlet vevs, lie within the experimental bounds. We scan over all possible configurations, and show that only a small class of U(1) charge assignments and matter distributions satisfy all the requirements. The solutions give rise to the exact MSSM spectrum with realistic quark and lepton Yukawa textures, which are consistent with the CKM and PMNS mixing matrices. We also discuss the geometric realization of these models, and provide pointers to the class of elliptic fibrations with good phenomenological properties.

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arXiv2014

Tate Trees for Elliptic Fibrations with Rank one Mordell-Weil group

U(1) symmetries play a central role in constructing phenomenologically viable F-theory compactifications that realize Grand Unified Theories (GUTs). In F-theory, gauge symmetries with abelian gauge factors are modeled by singular elliptic fibrations with additional rational sections, i.e. a non-trivial Mordell-Weil rank. To determine the full scope of possible low energy theories with abelian gauge factors, which allow for an F-theory realization, it is central to obtain a comprehensive list of all singular elliptic fibrations with extra sections. We answer this question for the case of one abelian factor by applying Tate's algorithm to the elliptic fiber realized as a quartic in the weighted projective space P^{(1,1,2)}, which guarantees, in addition to the zero section, the existence of an additional rational section. The algorithm gives rise to a tree-like enhancement structure, where each fiber is characterized by a Kodaira fiber type, that governs the non-abelian gauge factor, and the separation of the two sections. We determine Tate-like forms for elliptic fibrations with one extra section for all Kodaira fiber types. In addition to standard Tate forms that are determined by the vanishing order of the coefficient sections in the quartic (so-called canonical models),the algorithm also gives rise to fibrations that require non-trivial relations among the coefficient sections. Such non-canonical models have phenomenologically interesting properties, as they allow for a richer charged matter content, and thus codimension two fiber structure, than the canonical models that have been considered thus far in the literature. As an application we determine the complete set of codimension one fibers types, matter spectra, both canonical and non-canonical, for SU(5) x U(1) models.

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