scholarly journals Automatic enhancement in 6D supergravity and F-theory models

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikhil Raghuram ◽  
Washington Taylor ◽  
Andrew P. Turner
Keyword(s):  
Gauge Group ◽  
Theory Model ◽  
Matter Content ◽  
Exotic Matter ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Prior Literature

Abstract 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.

scholarly journals Classifying bases for 6D F-theory models

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
David Morrison ◽  
Washington Taylor
Keyword(s):  
Gauge Group ◽  
Geometric Structure ◽  
Theory Model ◽  
Matter Content ◽  
Tensor Fields ◽  
Base Surface ◽  
Canonical Class ◽  
Gauge Algebra ◽  
Simple Class ◽  
Simple Features

AbstractWe classify six-dimensional F-theory compactifications in terms of simple features of the divisor structure of the base surface of the elliptic fibration. This structure controls the minimal spectrum of the theory. We determine all irreducible configurations of divisors (“clusters”) that are required to carry nonabelian gauge group factors based on the intersections of the divisors with one another and with the canonical class of the base. All 6D F-theory models are built from combinations of these irreducible configurations. Physically, this geometric structure characterizes the gauge algebra and matter that can remain in a 6D theory after maximal Higgsing. These results suggest that all 6D supergravity theories realized in F-theory have a maximally Higgsed phase in which the gauge algebra is built out of summands of the types su(3), so(8), f4, e6, e8, e8, (g2 ⊕ su(2)); and su(2) ⊕ so(7) ⊕ su(2), with minimal matter content charged only under the last three types of summands, corresponding to the non-Higgsable cluster types identified through F-theory geometry. Although we have identified all such geometric clusters, we have not proven that there cannot be an obstruction to Higgsing to the minimal gauge and matter configuration for any possible F-theory model. We also identify bounds on the number of tensor fields allowed in a theory with any fixed gauge algebra; we use this to bound the size of the gauge group (or algebra) in a simple class of F-theory bases.

scholarly journals Higher-form symmetries of 6d and 5d theories

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Lakshya Bhardwaj ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Matter Content ◽  
Gauge Fields ◽  
Symmetry Groups ◽  
Abelian Gauge ◽  
Superconformal Field Theories ◽  
Supersymmetric Gauge ◽  
Web Construction

Abstract We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

scholarly journals Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds

2021 ◽  
Vol 36 (03) ◽  
pp. 2150027
Author(s):  
Yusuke Kimura
Keyword(s):  
Gauge Group ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Text Type ◽  
Double Covers

In this paper, we analyze gauge groups in six-dimensional [Formula: see text] F-theory models. We construct elliptic Calabi–Yau 3-folds possessing various singularity types as double covers of “1/2 Calabi–Yau 3-folds,” a class of rational elliptic 3-folds, by applying the method discussed in a previous study to classify the singularity types of the 1/2 Calabi–Yau 3-folds. One to three U(1) factors are formed in six-dimensional F-theory on the constructed Calabi–Yau 3-folds. The singularity types of the constructed Calabi–Yau 3-folds corresponding to the non-Abelian gauge group factors in six-dimensional F-theory are deduced. The singularity types of the Calabi–Yau 3-folds constructed in this work consist of [Formula: see text]- and [Formula: see text]-type singularities.

scholarly journals Magnetic lattices for orthosymplectic quivers

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Antoine Bourget ◽  
Julius F. Grimminger ◽  
Amihay Hanany ◽  
Rudolph Kalveks ◽  
Marcus Sperling ◽  
...  
Keyword(s):  
Gauge Group ◽  
Moduli Spaces ◽  
Hilbert Series ◽  
Matter Content ◽  
Coulomb Branch ◽  
Gauge Groups ◽  
Orbit Closures ◽  
Littlewood Polynomials ◽  
Monopole Operators ◽  
Crucial Ingredient

Abstract For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the choice of the precise gauge group becomes crucial when the magnetic lattice of the theory is considered. This question is addressed in the context of Coulomb branches for 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories, which are moduli spaces of dressed monopole operators. We compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers for different choices of gauge groups, including diagonal quotients of the product gauge group of individual factors, where the quotient is by a trivially acting subgroup. Choosing different such diagonal groups results in distinct Coulomb branches, related as orbifolds. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions 4, 5, and 6. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials.

scholarly journals Unraveling Spontaneously Broken Abelian Chern-Simons Theories

1997 ◽  
Vol 12 (06) ◽  
pp. 1013-1022 ◽  
Author(s):  
Mark de Wild Propitius
Keyword(s):  
Recent Work ◽  
Gauge Group ◽  
Direct Product ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Spontaneous Breakdown ◽  
Chern Simons

In this talk I describe recent work (hep-th/9606029) in which I classified all conceivable 2+1 dimensional Chern-Simons (CS) theories with continuous compact abelian gauge group or finite gauge group. The CS theories with finite abelian gauge group that can be obtained from the spontaneous breakdown of a CS theory with gauge group the direct product of various compact U(1) gauge groups were also identified. Those that can not be reached in this was are actually the most interesting since they lead to nonabelian pheomena such as nonabelian braid statistics, Alice fluxes and Cheshire charges and quite generally lead to dualities with 2+1 dimensional theories with a nonabelian finite gauge group.

scholarly journals Exploring the landscape of CHL strings on Td

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Dynkin Diagram ◽  
Fundamental Groups ◽  
Computer Algorithms ◽  
Abelian Gauge ◽  
Reduced Rank ◽  
Systematic Exploration ◽  
String Models ◽  
Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

scholarly journals On the quantization of Seiberg-Witten geometry

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nathan Haouzi ◽  
Jihwan Oh
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Partition Function ◽  
Flat Space ◽  
Matter Content ◽  
Gauge Groups ◽  
Space Limit ◽  
Two Parameters ◽  
Double Quantization ◽  
Quantization Parameters

Abstract We propose a double quantization of four-dimensional $$ \mathcal{N} $$ N = 2 Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by Nekrasov [1]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called Ω-background on ℝ4, in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.

scholarly journals A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 393
Author(s):  
Jan F. Haase ◽  
Luca Dellantonio ◽  
Alessio Celi ◽  
Danny Paulson ◽  
Angus Kan ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Gauge Theories ◽  
Hamiltonian Formulation ◽  
Mcmc Methods ◽  
Continuous Limit ◽  
Abelian Gauge ◽  
Gauge Groups

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2+1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

THE ADLER-BARDEEN THEOREM FOR THE AXIAL U(1) ANOMALY IN A GENERAL NON-ABELIAN GAUGE THEORY

1987 ◽  
Vol 02 (02) ◽  
pp. 385-407 ◽  
Author(s):  
CLAUDIO LUCCHESI ◽  
OLIVIER PIGUET ◽  
KLAUS SIBOLD
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Axial Current ◽  
Compact Lie Group ◽  
Zero Energy ◽  
Abelian Gauge ◽  
Regularization Scheme ◽  
Abelian Gauge Theory ◽  
Abelian Case ◽  
Finiteness Properties

A general, regularization-scheme-independent proof of the nonrenormalization theorem for the anomaly of a U(1) axial current in a renormalizable gauge theory is presented. The gauge group may be an arbitrary compact Lie group. The validity of the theorem is traced back to some finiteness properties allowing for a well defined but particular choice of the anomaly operators. Whereas in the case of a purely Abelian gauge group this choice amounts to a physically reasonable normalization at zero energy, the general non-Abelian case awaits a deeper understanding.

ENERGY REPRESENTATIONS OF INFINITE DIMENSIONAL GAUGE GROUPS IN NONCOMMUTATIVE GEOMETRY

1994 ◽  
Vol 05 (03) ◽  
pp. 329-348
Author(s):  
JEAN MARION
Keyword(s):  
Gauge Group ◽  
Noncommutative Geometry ◽  
Von Neumann Algebra ◽  
Linear Operators ◽  
Consistent Theory ◽  
Bounded Linear ◽  
Von Neumann ◽  
Gauge Groups ◽  
Infinite Dimensional ◽  
Involutive Algebra

Let M be a compact smooth manifold, let [Formula: see text] be a unital involutive subalgebra of the von Neumann algebra £ (H) of bounded linear operators of some Hilbert space H, let [Formula: see text] be the unital involutive algebra [Formula: see text], let [Formula: see text] be an hermitian projective right [Formula: see text]-module of finite type, and let [Formula: see text] be the gauge group of unitary elements of the unital involutive algebra [Formula: see text] of right [Formula: see text]-linear endomorphisms of [Formula: see text]. We first prove that noncommutative geometry provides the suitable setting upon which a consistent theory of energy representations [Formula: see text] can be built. Three series of energy representations are constructed. The first consists of energy representations of the gauge group [Formula: see text], [Formula: see text] being the group of unitary elements of [Formula: see text], associated with integrable Riemannian structures of M, and the second series consists of energy representations associated with (d, ∞)-summable K-cycles over [Formula: see text]. In the case where [Formula: see text] is a von Neumann algebra of type II 1 a third series is given: we introduce the notion of regular quasi K-cycle, we prove that regular quasi K-cycles over [Formula: see text] always exist, and that each of them induces an energy representation.

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