arXiv subjects

Natalia Saulina

Publications and source records attributed to Natalia Saulina.

At least 19 recordsLinked to original sources

arXiv2014

Coisotropic Branes in Toric Calabi-Yau 3-folds

We study disk-instantons ending on coisotropic branes preserved by real torus action in toric Calabi-Yau 3-folds. In particular, we find fermion zero modes on disk multi-covers ending on a coisotropic brane in local P^1 geometry with normal bundle (-a,a-2). It turns out that, independent of a, disk multi-cover formula is the same as for disks ending on a Lagrangian brane in resolved conifold. We further construct an example of a coisotropic brane in Calabi-Yau 3-fold used in geometric engineering of 4d N=2 SU(K) gauge theory, where this brane provides a surface defect.

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arXiv2014

Spectral networks and higher web-like structures

We derive traffic rule for spectral networks for A_2 theory for Riemann surface with punctures and use it to study in details the moduli space M of flat GL(3,C) connections on P^1 with 3 full punctures. We apply the simplified traffic rule to find the global description of M as the fibration with symplectic fibers and to study the space of line defects in 4d theory corresponding to the conformal point in the base of M. We define higher web-like structures, not previously discussed in the literature. They give rise to line defects independent of the defects corresponding to the traces of holonomies.

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arXiv2012

Global Gluing and G-flux

Local models that capture the 7-brane physics of F-theory compactifications for supersymmetric GUTs are conveniently described in terms of an E_8 gauge theory in the presence of a Higgs bundle. Though the Higgs bundle data is usually determined by the local geometry and G-flux, additional gluing data must be specified whenever the Higgs bundle spectral cover is not smooth. In this paper, we argue that this additional information is determined by data of the M-theory 3-form that is not necessarily captured by the cohomology class of the G-flux. More specifically, we show that when the 3-form is specified in terms of a line bundle on a spectral divisor, which is a global extension of the Higgs bundle spectral cover, the gluing data of the local model is uniquely determined in a way that ensures agreement with Heterotic results whenever a Heterotic dual exists.

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arXiv2012

OPE of Wilson-'t Hooft operators in N=4 and N=2 SYM with gauge group G=PSU(3)

We compute the simplest non-trivial Operator Product Expansion of Wilson-'t Hooft loop operators in N=4 and N=2 Super-Yang-Mills theory with gauge group G=PSU(3). This amounts to finding the Euler characters of certain vector bundles, describing electric degrees of freedom of loop operators entering the OPE, over moduli spaces of BPS states in the presence of loop operators.

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arXiv2011

A note on Wilson-'t Hooft operators

We find the basic ingredients required to compute the Operator Product Expansion of Wilson-'t Hooft operators in N=4 super-Yang-Mills theory with gauge group G=PSU(3). These include the geometry of certain moduli spaces of BPS configurations in the presence of 't Hooft operators and vector bundles over them. The bundles arise in computing the OPE due to electric degrees of freedom in dyonic operators. We verify our results by reproducing the OPE of 't Hooft operators predicted by S-duality.

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arXiv2011

On G-flux, M5 instantons, and U(1)s in F-theory

Local aspects of singular F-theory compactifications for SUSY GUT model-building are fairly well understood in terms of Higgs bundles and their spectral data. Several global issues remain, however, including a description of G-fluxes, which are key to constructing chiral matter and stabilizing moduli, and the global realization of U(1) symmetries that can forbid phenomenologically unfavorable couplings. In this paper, we sharpen our earlier proposal for describing G-fluxes through "spectral divisors" and introduce a distinguished "Tate divisor", which can be used to describe both G-flux and U(1)s when present. As an application, we give a general discussion of M5-instanton contributions in the presence of G-flux and exemplify this in a concrete example, where we comment on the ability of instanton induced superpotential couplings to stabilize Kahler moduli.

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arXiv2011

A Note on G-Fluxes for F-theory Model Building

We propose a description of G-fluxes that induce chirality in 4-dimensional F-theory GUT spectra that is intrinsic to F-theory and does not rely on Heterotic/F-theory duality. Using this, we describe how to globally extend fluxes that have been constructed in a semi-local setting and obtain an F-theoretic formula for computing the chiral spectrum that they induce. Chirality computations agree with those from the semi-local Higgs bundle analysis for matter fields that are charged under the GUT-group, and hence with the standard Heterotic formulae where applicable. Finally, the relation of G-fluxes to SU(5)_{perp} bundles on the F-theory 4-fold is discussed and used to motivate a quantization rule that is consistent both with the Higgs bundle one as well as the Heterotic one when a Heterotic dual exists.

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arXiv2011

F-theory GUTs with U(1) Symmetries: Generalities and Survey

We study the structure of SU(5) F-theory GUT models that engineer additional U(1) symmetries. These are highly constrained by a set of relations observed by Dudas and Palti (DP) that originate from the physics of 4D anomaly cancellation. Using the DP relations, we find a general tension between unification and the suppression of dimension 5 proton decay when one or more U(1)'s are PQ symmetries and hypercharge flux is used to break the SU(5) GUT group. We then specialize to spectral cover models, whose global completions in F- theory we know how to construct. In that setting, we provide a technical derivation of the DP relations, construct spectral covers that yield all possible solutions to them, and provide a complete survey of spectral cover models for SU(5) GUTs that exhibit two U(1) symmetries.

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arXiv2010

Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory

We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT. The algebraic properties of the resulting 2d RCFT, such as the classification of symmetry-preserving boundary conditions, are expressed in terms of properties of the surface operator. We show that to every surface operator one may attach a Morita-equivalence class of symmetric Frobenius algebras in the ribbon category of bulk line operators. This provides a simple interpretation of the results of Fuchs, Runkel and Schweigert on the construction of 2d RCFTs from Frobenius algebras. We also show that every topological boundary condition in a 3d TFT gives rise to a commutative Frobenius algebra in the category of bulk line operators. We illustrate these general considerations by studying in detail surface operators in abelian Chern-Simons theory.

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arXiv2010

Topological boundary conditions in abelian Chern-Simons theory

We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From a mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern-Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.

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arXiv2009

Compact F-theory GUTs with U(1)_PQ

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level μterm, play an important role in scenarios for neutrino physics and gauge mediation that have been proposed in local F-theory model building. As demonstrated in arXiv:0906.4672, the presence of such a symmetry implies the existence of non-GUT exotics in the spectrum, when hypercharge flux is used to break the GUT group and to give rise to doublet-triplet splitting. These exotics are of precisely the right type to solve the unification problem in such F-theory models and might also comprise a non-standard messenger sector for gauge mediation. We present a detailed description of models with U(1)_PQ in the semi-local regime, which does not depend on details of any specific Calabi-Yau four-fold, and then specialize to the geometry of arXiv:0904.3932 to construct three-generation examples with the minimal allowed number of non-GUT exotics. Among these, we find a handful of models in which the D3-tadpole constraint can be satisfied without requiring the introduction of anti-D3-branes. Finally, because SU(5) singlets that carry U(1)_PQ charge may serve as candidate right-handed neutrinos or can be used to lift the exotics, we study their origin in compact models and motivate a conjecture for how to count their zero modes in a semi-local setting.

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arXiv2009

F-theory Compactifications for Supersymmetric GUTs

We construct a family of elliptically fibered Calabi-Yau four-folds Y_4 for F-theory compactifications that realize SU(5) GUTs in the low-energy limit. The three-fold base X_3 of these fibrations is almost Fano and satisfies the topological criteria required to ensure that the U(1)_Y gauge boson remains massless, while allowing a decoupling of GUT and Planck scale physics. We study generic features of these models and the ability to engineer three chiral generations of MSSM matter. Finally, we demonstrate that it is relatively easy to implement the topological conditions required to reproduce certain successful features of local F-theory models, such as the emergence of flavor hierarchies.

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arXiv2009

An Instanton Toolbox for F-Theory Model Building

Several dimensionful parameters needed for model building can be engineered in a certain class of SU(5) F-theory GUTs by adding extra singlet fields which are localized along pairwise intersections of D7-branes. The values of these parameters, however, depend on dynamics external to the GUT which causes the singlets to acquire suitable masses or expectation values. In this note, we demonstrate that D3-instantons which wrap the same 4-cycle as one of the intersecting D7's can provide precisely the needed dynamics to generate several important scales, including the supersymmetry-breaking scale and the right-handed neutrino mass. Furthermore, these instantons seem unable to directly generate the μterm suggesting that, at least in this class of models, it should perhaps be tied to one of the other scales in the problem. More specifically, we study the simple system consisting of a pair of D7-branes wrapping del Pezzo surfaces which intersect along a curve $Σ$ of genus 0 or 1 and classify all instanton configurations which can potentially contribute to the superpotential. This allows one to formulate topological conditions which must be imposed on Σfor various model-building applications. Along the way, we also observe that the construction of arXiv:0808.1286 which engineers a linear superpotential in fact realizes an O'Raifeartaigh model at the KK scale whose 1-loop Coleman-Weinberg potential generically leads to a metastable, long-lived SUSY-breaking vacuum.

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arXiv2009

Instantons and SUSY breaking in F-theory

We study instanton contributions to the superpotential of local F-theory compactifications which could potentially be used to engineer models of dynamical supersymmetry breaking. These instantons correspond to Euclidean 3-branes which form a threshold bound state with spacetime filling 7-branes. In certain cases, their contributions to the effective 4d superpotential can be determined in both perturbative string theory as well as directly via the topologically twisted theory on the 3-brane worldvolume, and in all cases we observe an exact match between these results. We further present an instanton generated Polonyi-like model, and characterize subleading corrections to the superpotential which arise from multi-instantons. We also study instanton contributions to 4d pure N=1 SU(N) gauge theory realized by a stack of 7-branes wrapping a rigid 4-cycle and find that there is a non-trivial contribution to the glueball superpotential from the single instanton sector. This correction is absent in the purely 4d theory and could conceivably be used either to stabilize moduli or to break supersymmetry.

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arXiv2009

Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs

We analyze constraints for embedding local SU(5) F-theory GUTs into consistent compactifications and construct explicit three-generation models based on the geometry of arXiv:0904.3932. The key tool for studying constraints in this problem when there is an underlying E_8 structure is the spectral cover, which encodes all of the symmetries that fix the allowed couplings in the superpotential, as well as the consistent, supersymmetric G-fluxes. Imposing phenomenological requirements such as the existence of three generations, top and bottom Yukawa couplings, good flavor structure and absence of exotics and of a tree-level mu-term, we derive stringent constraints on the allowed spectral covers. The resulting spectral covers are in conflict with the neutrino scenarios that have been studied in local F-theory models unless we allow for the possibility of additional charged fields, perhaps playing the role of gauge messengers, that do not comprise complete GUT multiplets. Quite remarkably, the existence of additional incomplete GUT multiplets below the GUT scale is necessary for consistency with gauge coupling "unification", as their effect on weak scale couplings can precisely cancel that of the internal hypercharge flux, which distorts the gauge couplings already at M_GUT.

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arXiv2009

Stringy Instantons and Quiver Gauge Theories

We explore contributions to the 4D effective superpotential which arise from Euclidean D3 branes (``instantons'') that intersect space-filling D-branes. These effects can perturb the effective field theory on the space-filling branes by nontrivial operators composed of charged matter fields, changing the vacuum structure in a qualitative way in some examples. Our considerations are exemplified throughout by a careful study of a fractional brane configuration on a del Pezzo surface.

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arXiv2009

Gauge Mediation in F-Theory GUT Models

We study a simple framework for gauge-mediated supersymmetry-breaking in local GUT models based on F-theory 7-branes and demonstrate that a mechanism for solving both the μand μ/B_μ problems emerges in a natural way. In particular, a straightforward coupling of the messengers to the Higgs sector leads to a geometry which not only provides us with an approximate U(1)_{PQ} symmetry that forbids the generation of μat the GUT scale, it also forces the SUSY-breaking spurion field to carry a nontrivial PQ charge. This connects the breaking of SUSY to the generation of μso that the same scale enters both. Moreover, the messenger sector naturally realizes the D3-instanton triggered Polonyi model of arXiv:0808.1286 so this scale is exponentially suppressed relative to M_{GUT}. The effective action at low scales is in fact precisely of the form of the "sweet spot supersymmetry" scenario studied by Ibe and Kitano in arXiv:0705.3686.

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arXiv2009

Chern-Simons-Rozansky-Witten topological field theory

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kahler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern-Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.

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