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In this work, we study F-theory compactifications on manifolds. Such geometries, which we study in both 4- and 6dimensions, are both ubiquitous within the set of Calabi-Yau manifolds and play a crucial role in heterotic/F-theory duality. We discuss the most general formulation of P1-bundles of this type, as well as fibrations which degenerate at higher codimension loci. In the course of this study, we find a number of new phenomena. For example, in both 4- and 6-dimensions we find transitions whereby the base of a P1-bundle can change nature, or "jump ", at certain loci in complex structure moduli space. We discuss the implications of this jumping for the associated heterotic duals. We argue that P1-bundles with only rational sections lead to heterotic duals where the Calabi-Yau manifold is elliptically fibered over the section of the P1 bundle, and not its base. As expected, we see that degenerations of the P1 fibration of the F-theory base correspond to 5-branes in the dual heterotic physics, with the exception of cases in which the fiber degenerations exhibit monodromy. Along the way, we discuss a set of useful formulae and tools for describing F-theory compactifications on this class of Calabi-Yau manifolds.

We analyzed bichromatic and polychromatic stimulated forces for laser cooling and trapping of Yb atoms using only the narrow S-1(0) -> P-3(1) transition. Our model is based on numerical solutions of optical Bloch equations for two-level atoms driven by multiple time-dependent fields combined with Monte Carlo simulations, which account for realistic experimental conditions such as atomic beam divergence, geometry, and Gaussian laser modes. Using 1 W of laser power, we predict a loading rate of 10(8) atoms/s into a 556-nm magneto-optical trap (MOT) with a slowing force of approximate to 60F(rad). We show that a square-wave modulation can produce similar stimulated forces with almost twice the velocity range and improve the MOT loading rate of Yb atoms by up to 70%.

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group (SU(3) × SU(2) × U(1))/ℤ6 and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with U(1) gauge symmetry and charges q ≤ 4 previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetič, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group G and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here.

We observe that in many F-theory models, tuning a specific gauge group G and matter content M under certain circumstances leads to an automatic enhancement to a larger gauge group G′ ⊃ G and matter content M′ ⊃ M. We propose that this is true for any theory G, M whenever there exists a containing theory G′, M′ that cannot be Higgsed down to G, M. We give a number of examples including non-Higgsable gauge factors, nonabelian gauge factors, abelian gauge factors, and exotic matter. In each of these cases, tuning an F-theory model with the desired features produces either an enhancement or an inconsistency, often when the associated anomaly coefficient becomes too large. This principle applies to a variety of models in the apparent 6D supergravity swampland, including some of the simplest cases with U(1) and SU(N) gauge groups and generic matter, as well as infinite families of U(1) models with higher charges presented in the prior literature, potentially ruling out all these apparent swampland theories.

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group (SU(3) × SU(2) × U(1))/ℤ6 and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with U(1) gauge symmetry and charges q <= 4 previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetic, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group G and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2018., Cataloged from PDF version of thesis., Includes bibliographical references (pages 409-419)., F-theory has emerged as a powerful tool for string compactification, as it can realize a number of string vacua with varying gauge groups, charged matter, and other properties. However, some aspects of F-theory are still not completely understood, particularly those involving charged matter. There is currently no complete classification of all the charged matter representations that can occur in F-theory. Moreover, constructing models with a desired charge spectrum can be difficult. Some simple representations, such as the fundamental representations of nonabelian gauge groups, appear automatically in F-theory constructions. But representations beyond these simple types appear only in algebraically intricate constructions, and few techniques exist to systematically construct models with these more unusual representations. This thesis therefore focuses on gauge groups and charged matter in F-theory models. On the one hand, we examine whether models with various representations can be constructed in F-theory and discuss systematic methods for deriving them. We also describe interesting physical phenomena that occur in theories with less common representations. After briefly reviewing string theory and F-theory, we begin by describing a novel kind of transition between string vacua that changes the matter content of the model without changing the gauge group or other parts of the spectrum. These "matter transitions" are realized by passing through superconformal theories at the transition point. We first discuss how such transitions can be motivated from supergravity considerations. We then illustrate how the transitions manifest themselves in dual F-theory and heterotic models. We also explicitly analyze the duality between the heterotic and F-theory constructions, as the models we consider serve as nontrivial examples of heterotic/F-theory duality in their own right. We then turn to the topic of higher-genus representations in F-theory. Certain representations occur, by Nikhil Raghuram., Ph. D.

We show that massless fields with large abelian charges (up to at least q = 21) can be constructed in 6D F-theory models with a U(1) gauge group. To show this, we explicitly construct F-theory Weierstrass models with nonabelian gauge groups that can be broken to U(1) theories with a variety of large charges. Determining the maximum abelian charge allowed in such a theory is key to eliminating what seems currently to be an infinite swampland of apparently consistent U(1) supergravity theories with large charges.

We analyze exotic matter representations that arise on singular seven-brane configurations in F-theory. We develop a general framework for analyzing such representations, and work out explicit descriptions for models with matter in the 2-index and 3-index symmetric representations of SU(N) and SU(2) respectively, associated with double and triple point singularities in the seven-brane locus. These matter representations are associated with Weierstrass models whose discriminants vanish to high order thanks to nontrivial cancellations possible only in the presence of a non-UFD algebraic structure. This structure can be described using the normalization of the ring of intrinsic local functions on a singular divisor. We consider the connection between geometric constraints on singular curves and corresponding constraints on the low-energy spectrum of 6D theories, identifying some new examples of apparent “swampland” theories that cannot be realized in F-theory but have no apparent low-energy inconsistency. Keywords: F-Theory; Differential and Algebraic Geometry; Supergravity Models; Superstring Vacua, National Science Foundation (U.S.) (Grant PHY-1066293)

We show that massless fields with large abelian charges (up to at least q = 21) can be constructed in 6D F-theory models with a U(1) gauge group. To show this, we explicitly construct F-theory Weierstrass models with nonabelian gauge groups that can be broken to U(1) theories with a variety of large charges. Determining the maximum abelian charge allowed in such a theory is key to eliminating what seems currently to be an infinite swampland of apparently consistent U(1) supergravity theories with large charges.

This paper analyzes U(1) F-theory models admitting matter with charges q = 3 and 4. First, we systematically derive a q = 3 construction that generalizes the previous q = 3 examples. We argue that U(1) symmetries can be tuned through a procedure reminiscent of the SU(N ) and Sp(N ) tuning process. For models with q = 3 matter, the components of the generating section vanish to orders higher than 1 at the charge-3 matter loci. As a result, the Weierstrass models can contain non-UFD structure and thereby deviate from the standard Morrison-Park form. Techniques used to tune SU(N ) models on singular divisors allow us to determine the non-UFD structures and derive the q = 3 tuning from scratch. We also obtain a class of a q=4 models by deforming a prior U(1) × U(1) construction. To the author’s knowledge, this is the first published F-theory example with charge-4 matter. Finally, we discuss some conjectures regarding models with charges larger than 4. Keywords: F-Theory, Superstring Vacua

We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.

We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three-index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction., United States. Department of Energy (contract #DE-SC00012567), National Science Foundation (U.S.) (Grant No. PHY-1066293)